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Deck 2: Quadratic and Other Special Functions
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Question
Write the equation 
in general form.
A)
B)
C)
D)
E)
in general form. A)
B)
C)
D)
E)
Question
Find the exact real solutions of the equation 
, if they exist.
A)
and 
B)
and 
C)
and 
D)
and 
E)
and 
, if they exist. A)
and B)
and C)
and D)
and E)
and Question
The amount of airborne particulate pollution p from a power plant depends on the wind speed s, among other things, with the relationship between p and s approximated by 
. Find the value of s that will make 
.
A)
B)
C)
D)
E)
. Find the value of s that will make . A)
B)
C)
D)
E)
Question
Multiply both sides of the equation 
by the LCD, and then solve the resulting quadratic equation.
A)
B)
C)
D)
E)
by the LCD, and then solve the resulting quadratic equation. A)
B)
C)
D)
E)
Question
The sensitivity S to a drug is related to the dosage size by 
, where x is the dosage size in milliliters. Determine all dosages that yield 0 sensitivity.
A)
milliliters, 
milliliters
B)
milliliters, 
milliliters
C)
milliliters, 
milliliters
D)
milliliters, 
milliliters
E)
milliliters
, where x is the dosage size in milliliters. Determine all dosages that yield 0 sensitivity. A)
milliliters, millilitersB)
milliliters, millilitersC)
milliliters, millilitersD)
milliliters, millilitersE)
milliliters Question
Solve the equation 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Solve the equation by using the quadratic formula. Give real answers rounded to two decimal places. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
If a ball is thrown upward at 80 feet per second from the top of a building that is 100 feet high, the height of the ball can be modeled by 
, where t is the number of seconds after the ball is thrown. How long after it is thrown is the height 100 feet?
A)
seconds
B)
seconds
C)
seconds
D)
seconds
E)
seconds
, where t is the number of seconds after the ball is thrown. How long after it is thrown is the height 100 feet?A)
secondsB)
secondsC)
secondsD)
secondsE)
seconds Question
Find the exact real solutions of the equation 
, if they exist.
A)
and 
B)
and 
C)
and 
D)
and 
E) Real solutions do not exist.
, if they exist. A)
and B)
and C)
and D)
and E) Real solutions do not exist.
Question
Find the exact real solutions of the equation 
, if they exist.
A)
and 
B)
and 
C)
and 
D)
and 
E)
and 
, if they exist. A)
and B)
and C)
and D)
and E)
and Question
Solve the equation by using a graphing utility. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the exact real solutions to the equation, if they exist. 
A)
B)
C)
D)
E) no real solutions
A)
B)
C)
D)
E) no real solutions
Question
Write the equation 
in general form.
A)
B)
C)
D)
E)
in general form. A)
B)
C)
D)
E)
Question
Solve the equation 
by factoring.
A)
B)
C)
D)
E)
by factoring. A)
B)
C)
D)
E)
Question
Solve the equation by using the quadratic formula. Give real solutions only. 
A)
B)
C)
D) no real solutions
E)
A)
B)
C)
D) no real solutions
E)
Question
Solve the equation below using quadratic methods. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the equation 
by first multiplying by the LCD, and then solving the resulting equation.
A)
B)
C)
D)
E)
by first multiplying by the LCD, and then solving the resulting equation. A)
B)
C)
D)
E)
Question
Find the exact real solutions to the equation, if they exist. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
If the profit from the sale of x units of a product is 
, what level(s) of production will yield a profit of $1,000?
A) less 15 units of production.
B) more than 80 units of production.
C) 95 units of production.
D) 65 units of production.
E) 15 or 80 units of production.
, what level(s) of production will yield a profit of $1,000? A) less 15 units of production.
B) more than 80 units of production.
C) 95 units of production.
D) 65 units of production.
E) 15 or 80 units of production.
Question
Solve the equation 
by using a graphing utility. Round your answers to two decimal places.
A)
and 
B)
and 
C)
and 
D)
and 
E)
and 
by using a graphing utility. Round your answers to two decimal places. A)
and B)
and C)
and D)
and E)
and Question
Determine whether the function's vertex is a maximum point or a minimum point and find the coordinates of this point. 
A) vertex:
, a minimum point
B) vertex:
, a maximum point
C) vertex:
, a minimum point
D) vertex:
, a maximum point
E) vertex:
, a maximum point
A) vertex:
, a minimum pointB) vertex:
, a maximum pointC) vertex:
, a minimum pointD) vertex:
, a maximum pointE) vertex:
, a maximum point Question
Find the average rate of change of the function between the given values of x. 
between 
and 
.
A) 15
B) 50
C) 0
D) -6
E) 100
between and .
A) 15
B) 50
C) 0
D) -6
E) 100
Question
How is the graph of 
shifted to obtain the graph of the function 
?
A) shifted 12 units to the left and 13 units up
B) shifted 12 units to the right and 13 units down
C) shifted 144 units to the left and 13 units up
D) shifted 24 units to the right and 13 units down
E) shifted 12 units to the right and 13 units up
shifted to obtain the graph of the function ? A) shifted 12 units to the left and 13 units up
B) shifted 12 units to the right and 13 units down
C) shifted 144 units to the left and 13 units up
D) shifted 24 units to the right and 13 units down
E) shifted 12 units to the right and 13 units up
Question
Find the vertex of the graph of the equation 
. Round your answer to two decimal places.
A)
B)
C)
D)
E)
. Round your answer to two decimal places. A)
B)
C)
D)
E)
Question
A fissure in the earth appeared after an earthquake. To measure its vertical depth, a stone was dropped into it, and the sound of the stone's impact was heard 3.3 seconds later. The distance (in feet) the stone fell is given by 
, and the distance (in feet) the sound traveled is given by 
. In these equations, the distances traveled by the sound and the stone are the same, but their times are not. Using the fact that the total time is 3.3 seconds, find the depth of the fissure. Round your answer to two decimal places.
A) 94.19 feet
B) 91.00 feet
C) 121.98 feet
D) 126.38 feet
E) 126.48 feet
, and the distance (in feet) the sound traveled is given by . In these equations, the distances traveled by the sound and the stone are the same, but their times are not. Using the fact that the total time is 3.3 seconds, find the depth of the fissure. Round your answer to two decimal places. A) 94.19 feet
B) 91.00 feet
C) 121.98 feet
D) 126.38 feet
E) 126.48 feet
Question
Determine what value of x gives the optimal value of the function, and determine the optimal (maximum or minimum) value. Round your answers to two decimal places. 
A) optimal value of x: 0, optimal value: 1.00
B) optimal value of x: -1.13, optimal value: 0.75
C) optimal value of x: 1.50, optimal value: -1.50
D) optimal value of x: -0.75, optimal value: -1.13
E) optimal value of x: 0.75, optimal value: -1.13
A) optimal value of x: 0, optimal value: 1.00
B) optimal value of x: -1.13, optimal value: 0.75
C) optimal value of x: 1.50, optimal value: -1.50
D) optimal value of x: -0.75, optimal value: -1.13
E) optimal value of x: 0.75, optimal value: -1.13
Question
Find the vertex and then determine the range of the function. 
A) all values greater than or equal to 67
B) all values less than or equal to 63
C) all values greater than or equal to 10
D) all values less than or equal to 85
E) all values less than or equal to 67
A) all values greater than or equal to 67
B) all values less than or equal to 63
C) all values greater than or equal to 10
D) all values less than or equal to 85
E) all values less than or equal to 67
Question
Sketch the graph of the following function by using graphing calculator. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Find the vertex of the graph of the equation 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find the zeros, if any exist. Round your answers to two decimal places. 
A) zeros at -2.17 and -7.83
B) zeros at 0 and 10.00
C) zeros at 11.00 and -21.00
D) no zeros
E) zeros at 0 and 27.00
A) zeros at -2.17 and -7.83
B) zeros at 0 and 10.00
C) zeros at 11.00 and -21.00
D) no zeros
E) zeros at 0 and 27.00
Question
Find the x-intercepts, if any exist. Round your answers to two decimal places. 
A) x-intercepts:
, 
B) x-intercepts:
, 
C) x-intercepts:
, 
D) x-intercepts:
, 
E) no x-intercepts
A) x-intercepts:
, B) x-intercepts:
, C) x-intercepts:
, D) x-intercepts:
, E) no x-intercepts
Question
The time t, in seconds, that it takes a 2005 Corvette to accelerate to x mph can be described by 
. How fast is the Corvette going after 9.08 seconds? Give your answer to the nearest tenth.
A) 97.1 mph
B) 98.1 mph
C) 100.1 mph
D) 118.9 mph
E) 119.4 mph
. How fast is the Corvette going after 9.08 seconds? Give your answer to the nearest tenth. A) 97.1 mph
B) 98.1 mph
C) 100.1 mph
D) 118.9 mph
E) 119.4 mph
Question
Use a graphing utility to approximate the solutions to 
. Round your answers to two decimal places. 
A)
B)
C)
D)
E)
. Round your answers to two decimal places. A)
B)
C)
D)
E)
Question
Determine whether the vertex of the graph of the following function is a maximum point or a minimum point. Also find the coordinates of the vertex. 
A) vertex:
, a maximum point
B) vertex:
, a minimum point
C) vertex:
, a minimum point
D) vertex:
, a minimum point
E) vertex:
, a maximum point
A) vertex:
, a maximum pointB) vertex:
, a minimum pointC) vertex:
, a minimum pointD) vertex:
, a minimum pointE) vertex:
, a maximum point Question
Determine if the vertex of the graph of the equation is a maximum or minumim point. 
A) vertex is at a maximum point
B) vertex is at a minimum point
C) has no vertex
A) vertex is at a maximum point
B) vertex is at a minimum point
C) has no vertex
Question
Sketch the graph of the following function. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Use a graphing utility to find the vertex of the function. Round your answer to two decimal places. 
A) vertex:
B) vertex: origin
C) vertex:
D) vertex:
E) vertex:
A) vertex:
B) vertex: origin
C) vertex:
D) vertex:
E) vertex:
Question
Suppose that the percent of total personal income that is used to pay personal taxes is given by 
, where x is the number of years past 1990 (Source: Bureau of Economic Analysis, U.S. Department of Commerce). Find the year or years when the percent of total personal income used to pay personal taxes is 18 percent.
A) 2013
B) 2003
C) 2002
D) 2008
E) 2044
, where x is the number of years past 1990 (Source: Bureau of Economic Analysis, U.S. Department of Commerce). Find the year or years when the percent of total personal income used to pay personal taxes is 18 percent. A) 2013
B) 2003
C) 2002
D) 2008
E) 2044
Question
An equation that models the number of users of the Internet is 
million users, where x is the number of years past 1990 (Source: CyberAtlas, 1999). If the pattern indicated by the model remains valid, when does this model predict there will be 1,100 million users?
A) 2004
B) 2021
C) 2014
D) 2007
E) 2005
million users, where x is the number of years past 1990 (Source: CyberAtlas, 1999). If the pattern indicated by the model remains valid, when does this model predict there will be 1,100 million users? A) 2004
B) 2021
C) 2014
D) 2007
E) 2005
Question
The model for body-heat loss depends on the coefficient of convection K, which depends on wind speed v according to the equation 
where v is in miles per hour. Find the positive coefficient of convection when the wind speed is 29 mph. Round your answer to the nearest integer.
A)
B)
C)
D)
E)
where v is in miles per hour. Find the positive coefficient of convection when the wind speed is 29 mph. Round your answer to the nearest integer. A)
B)
C)
D)
E)
Question
The daily profit from the sale of a product is given by 
dollars. What is the maximum possible profit? Round intermediate calculations and final answer to the nearest dollar.
A) $1,701
B) $2,613
C) $808
D) $95
E) $185
dollars. What is the maximum possible profit? Round intermediate calculations and final answer to the nearest dollar. A) $1,701
B) $2,613
C) $808
D) $95
E) $185
Question
The supply function for a product is 
, while the demand function for the same product is 
. Find the market equilibrium point E(q, p). Round your final answer to two decimal places.
A)
B)
C)
D)
E)
, while the demand function for the same product is . Find the market equilibrium point E(q, p). Round your final answer to two decimal places. A)
B)
C)
D)
E)
Question
If the supply function for a commodity is 
and the demand function is 
, find the equilibrium quantity and equilibrium price. Round your final answer to two decimal places.
A)
B)
C)
D)
E)
and the demand function is , find the equilibrium quantity and equilibrium price. Round your final answer to two decimal places. A)
B)
C)
D)
E)
Question
When a stone is thrown upward, it follows a parabolic path given by a form of the equation 
. If 
represents ground level, find the equation of a stone that is thrown from ground level at 
and lands on the ground 130 units away if the stone reaches a maximum height of 130 units.
A)
B)
C)
D)
E)
. If represents ground level, find the equation of a stone that is thrown from ground level at and lands on the ground 130 units away if the stone reaches a maximum height of 130 units. A)
B)
C)
D)
E)
Question
Sketch the first quadrant portions of the following functions and estimate the market equilibrium point.
Supply:
Demand: 
A) 
B) 
C) 
D) 
E) 
Supply:
Demand: A)
B)
C)
D)
E)
Question
In 1995, America's 45 million Social Security recipients received a 2.6% cost-of-living increase, the second smallest increase in nearly 20 years, a reflection of lower inflation. The percent increase might be described by the function 
, where t is the number of years past 1980. In what year does the model predict the highest cost of living percent increase?
A) 1990
B) 2009
C) 1987
D) 1989
E) none of the above
, where t is the number of years past 1980. In what year does the model predict the highest cost of living percent increase? A) 1990
B) 2009
C) 1987
D) 1989
E) none of the above
Question
If the supply and demand functions for a commodity are given by 
and 
, what is the equilibrium price and what is the corresponding number of units supplied and demanded? Round your answer to two decimal places.
A)
B)
C)
D)
E)
and , what is the equilibrium price and what is the corresponding number of units supplied and demanded? Round your answer to two decimal places. A)
B)
C)
D)
E)
Question
A ball thrown vertically into the air has its height above ground given by 
, where t is in seconds and s is in feet. Find the maximum height of the ball.
A) 242 feet
B) 121 feet
C) 8 feet
D) 16 feet
E) 229 feet
, where t is in seconds and s is in feet. Find the maximum height of the ball. A) 242 feet
B) 121 feet
C) 8 feet
D) 16 feet
E) 229 feet
Question
The owner of a skating rink rents the rink for parties at $912 if 76 or fewer skaters attend, so that the cost per person is $12 if 76 attend. For each 5 skaters above 76, she reduces the price per skater by $0.50. Which table gives the revenue generated if 76, 86, and 96 skaters attend?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The daily profit from the sale of a product is given by 
dollars. What level of production maximizes profit?
A) production level of 100 units
B) production level of 10 units
C) production level of 5 units
D) production level of 50 units
E) production level of 95 units
dollars. What level of production maximizes profit? A) production level of 100 units
B) production level of 10 units
C) production level of 5 units
D) production level of 50 units
E) production level of 95 units
Question
If a firm has the following cost and revenue functions, find the break-even points. 
A) Break-even values are at
and 
units.
B) Break-even values are at
and 
units.
C) Break-even values are at
and 
units.
D) Break-even values are at
and 
units.
E) Break-even values are at
and 
units.
A) Break-even values are at
and units.B) Break-even values are at
and units.C) Break-even values are at
and units.D) Break-even values are at
and units.E) Break-even values are at
and units. Question
The supply function for a product is 
, while the demand function for the same product is 
. If a $22 tax is placed on production of the item, then the supplier passes this tax on by adding $22 to his selling price. Find the new equilibrium point E(q, p) for this product when the tax is passed on. (The new supply function is given by 
.) Round your final answer to two decimal places.
A)
B)
C)
D)
E)
, while the demand function for the same product is . If a $22 tax is placed on production of the item, then the supplier passes this tax on by adding $22 to his selling price. Find the new equilibrium point E(q, p) for this product when the tax is passed on. (The new supply function is given by .) Round your final answer to two decimal places. A)
B)
C)
D)
E)
Question
If the supply and demand functions for a commodity are given by 
and 
, respectively, find the price that will result in market equilibrium.
A) 41
B) 150
C) 33
D) 31
E) 25
and , respectively, find the price that will result in market equilibrium. A) 41
B) 150
C) 33
D) 31
E) 25
Question
The yield in bushels from a grove of orange trees is given by 
, where x is the number of orange trees per acre. How many trees will maximize the yield?
A) 1,500 trees
B) 3,000 trees
C) 800 trees
D) 1,550 trees
E) 750 trees
, where x is the number of orange trees per acre. How many trees will maximize the yield? A) 1,500 trees
B) 3,000 trees
C) 800 trees
D) 1,550 trees
E) 750 trees
Question
The total costs for a company are given by 
, and the total revenues are given by 
. Find the break-even points.
A) Break-even values are at x = 35 and x = 70 units.
B) Break-even values are at x = inf units.
C) Break-even values are at x = -inf units.
D) Break-even values are at x = 17.5 and x = 35 units.
E) Break-even values are at x = 70 units.
, and the total revenues are given by . Find the break-even points. A) Break-even values are at x = 35 and x = 70 units.
B) Break-even values are at x = inf units.
C) Break-even values are at x = -inf units.
D) Break-even values are at x = 17.5 and x = 35 units.
E) Break-even values are at x = 70 units.
Question
The sensitivity S to a drug is related to the dosage x in milligrams by 
. Use a graphing utility to determine what dosage gives maximum sensitivity.
A) 97
B) 235,225
C) 970, 0
D) 970
E) 485
. Use a graphing utility to determine what dosage gives maximum sensitivity. A) 97
B) 235,225
C) 970, 0
D) 970
E) 485
Question
A supply function has the equation is 
, and the demand function is decribed by the equation 
. Algebraically determine the equilibrium point for the supply and demand functions. Round your answer to two decimal places.
A)
B)
C)
D)
E)
, and the demand function is decribed by the equation . Algebraically determine the equilibrium point for the supply and demand functions. Round your answer to two decimal places. A)
B)
C)
D)
E)
Question
Solve 
for the function 
.
A)
B)
C)
D)
E) no real solutions
for the function . A)
B)
C)
D)
E) no real solutions
Question
Factor the function 
.
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
The daily profit from the sale of a product is given by 
dollars. What is the maximum possible profit? Round intermediate calculations and final answer to the nearest dollar.
A) $5,423
B) $16,685
C) $11,013
D) $137
E) $271
dollars. What is the maximum possible profit? Round intermediate calculations and final answer to the nearest dollar. A) $5,423
B) $16,685
C) $11,013
D) $137
E) $271
Question
Suppose a company has fixed costs of $27,000 and variable costs of 
dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is 
dollars per unit. Find the maximum revenue. Round your answer to the nearest cent.
A) Maximum revenue is $1,026.70.
B) Maximum revenue is $27,000.00.
C) Maximum revenue is $26,862.50.
D) Maximum revenue is $677,343.75.
E) Maximum revenue is $612.50.
dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is dollars per unit. Find the maximum revenue. Round your answer to the nearest cent. A) Maximum revenue is $1,026.70.
B) Maximum revenue is $27,000.00.
C) Maximum revenue is $26,862.50.
D) Maximum revenue is $677,343.75.
E) Maximum revenue is $612.50.
Question
Sketch the graph of the function 
.
A) 
B) 
C) 
D) 
E) 
. A)
B)
C)
D)
E)
Question
Assume that sales revenues, in millions, for Continental Divide Mining can be described by 
, where t is the number of years past 1992. Use the function to find the maximum revenue. Round your answers to three decimal places.
A) Maximum revenue is $9.463 million.
B) Maximum revenue is $5.971 million.
C) Maximum revenue is $3.672 million.
D) Maximum revenue is $3.851 million.
E) Maximum revenue is $16.986 million.
, where t is the number of years past 1992. Use the function to find the maximum revenue. Round your answers to three decimal places. A) Maximum revenue is $9.463 million.
B) Maximum revenue is $5.971 million.
C) Maximum revenue is $3.672 million.
D) Maximum revenue is $3.851 million.
E) Maximum revenue is $16.986 million.
Question
Form the profit function for the cost and revenue functions, where the total costs and total revenues are given by 
and 
.
A)
B)
C)
D)
E)
and . A)
B)
C)
D)
E)
Question
The graph of the profit function 
is given as follows. Consider the average rate of change of the profit from a to 400 where a lies to the left of 400. Does the average rate of change of the profit get closer to 0 or farther from 0 as a gets closer to 400? 
A) closer to 0
B) farther from 0
is given as follows. Consider the average rate of change of the profit from a to 400 where a lies to the left of 400. Does the average rate of change of the profit get closer to 0 or farther from 0 as a gets closer to 400? A) closer to 0
B) farther from 0
Question
If, in a monopoly market, the demand for a product is 
, and the revenue function is 
, where x is the number of units sold, what price will maximize revenue? Round your answer to the nearest cent.
A) Price that will maximize revenue is
.
B) Price that will maximize revenue is
.
C) Price that will maximize revenue is
.
D) Price that will maximize revenue is
.
E) Price that will maximize revenue is
.
, and the revenue function is , where x is the number of units sold, what price will maximize revenue? Round your answer to the nearest cent. A) Price that will maximize revenue is
.B) Price that will maximize revenue is
.C) Price that will maximize revenue is
.D) Price that will maximize revenue is
.E) Price that will maximize revenue is
. Question
Sketch the graph of the function 
.
A) 
B) 
C) 
D) 
E) 
. A)
B)
C)
D)
E)
Question
Given the profit function, 
, and that production is restricted to fewer than 75 units, find the break-even point(s). Round your answer to two decimal places.
A) Break-even value is at
units.
B) Break-even value is at
units.
C) Break-even value is at
units.
D) Break-even value is at
units.
E) Break-even value is at
units.
, and that production is restricted to fewer than 75 units, find the break-even point(s). Round your answer to two decimal places. A) Break-even value is at
units.B) Break-even value is at
units.C) Break-even value is at
units.D) Break-even value is at
units.E) Break-even value is at
units. Question
Find the maximum revenue for the revenue function 
. Round your answer to the nearest cent.
A) $84,008.93
B) $252,026.79
C) $48,005.10
D) $216,022.96
E) $253,026.79
. Round your answer to the nearest cent. A) $84,008.93
B) $252,026.79
C) $48,005.10
D) $216,022.96
E) $253,026.79
Question
Use a graphing calculator to graph the profit function 
.
A) 
B) 
C) 
D) 
E) 
. A)
B)
C)
D)
E)
Question
If a company has total costs 
, and total revenues given by 
, find the break-even points. Round your answers to two decimal places.
A) Break-even values are at
and 
units.
B) Break-even values are at
and 
units.
C) Break-even values are at
and 
units.
D) Break-even values are at
units.
E) Break-even values are at
and 
units.
, and total revenues given by , find the break-even points. Round your answers to two decimal places. A) Break-even values are at
and units.B) Break-even values are at
and units.C) Break-even values are at
and units.D) Break-even values are at
units.E) Break-even values are at
and units. Question
If total costs are 
and total revenues are 
, find the break-even points.
A) Break-even values are at
and 
units.
B) Break-even values are at
and 
units.
C) Break-even values are at
and 
units.
D) Break-even values are at
and 
units.
E) Break-even values are at
and 
units.
and total revenues are , find the break-even points. A) Break-even values are at
and units.B) Break-even values are at
and units.C) Break-even values are at
and units.D) Break-even values are at
and units.E) Break-even values are at
and units. Question
The profit function for a certain commodity is 
. Find the level of production that yields maximum profit, and find the maximum profit.
A) Production levels of 110 yields a maximum profit of $1,200.
B) Production levels of 110 yields a maximum profit of $1,825.
C) Production levels of 55 yields a maximum profit of $4,795.
D) Production levels of 55 yields a maximum profit of $3,025.
E) Production levels of 55 yields a maximum profit of $1,825.
. Find the level of production that yields maximum profit, and find the maximum profit. A) Production levels of 110 yields a maximum profit of $1,200.
B) Production levels of 110 yields a maximum profit of $1,825.
C) Production levels of 55 yields a maximum profit of $4,795.
D) Production levels of 55 yields a maximum profit of $3,025.
E) Production levels of 55 yields a maximum profit of $1,825.
Question
Sketch the graph of the function below. 
A) 
B) 
C) 
D) 
E) 
A)
B)
C)
D)
E)
Question
Sketch the graph of the function 
.
A) 
B) 
C) 
D) 
E) 
. A)
B)
C)
D)
E)
Question
Suppose a company has fixed costs of $26,000 and variable costs of 
dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is 
dollars per unit. Find the break-even points. Round your answer to the nearest cent.
A) Break-even values are at
and 
.
B) Break-even values are at
and 
.
C) Break-even values are at
and 
.
D) Break-even values are at
and 
.
E) Break-even values are at
and 
.
dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is dollars per unit. Find the break-even points. Round your answer to the nearest cent. A) Break-even values are at
and .B) Break-even values are at
and .C) Break-even values are at
and .D) Break-even values are at
and .E) Break-even values are at
and . Question
Assume that sales revenues for Continental Divide Mining can be described by 
, where t is the number of years past 1992. Use the function to determine the year in which maximum revenue occurs.
A) Maximum revenue occurred during 1998.
B) Maximum revenue occurred during 1992.
C) Maximum revenue occurred during 1997.
D) Maximum revenue occurred during 2003.
E) Maximum revenue occurred during 1991.
, where t is the number of years past 1992. Use the function to determine the year in which maximum revenue occurs. A) Maximum revenue occurred during 1998.
B) Maximum revenue occurred during 1992.
C) Maximum revenue occurred during 1997.
D) Maximum revenue occurred during 2003.
E) Maximum revenue occurred during 1991.
Question
Assume that costs and expenses for Continental Divide Mining can be described by 
and the sales revenue can be described by 
, where t is the number of years since the beginning of 1992. Find the year in which maximum profit occurs.
A) 2014
B) 1993
C) 2003
D) 2004
E) 1994
and the sales revenue can be described by , where t is the number of years since the beginning of 1992. Find the year in which maximum profit occurs. A) 2014
B) 1993
C) 2003
D) 2004
E) 1994
Question
Sketch the graph of the function 
.
A) 
B) 
C) 
D) 
E) 
. A)
B)
C)
D)
E)
Question
Sketch the graph of the function 
.
A) 
B) 
C) 
D) 
E) 
. A)
B)
C)
D)
E)
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Deck 2: Quadratic and Other Special Functions
1
Write the equation in general form.
A)
B)
C)
D)
E)
in general form. A)
B)
C)
D)
E)
2
Find the exact real solutions of the equation , if they exist.
A) and
B) and
C) and
D) and
E) and
, if they exist. A)
and B)
and C)
and D)
and E)
and and 3
The amount of airborne particulate pollution p from a power plant depends on the wind speed s, among other things, with the relationship between p and s approximated by . Find the value of s that will make .
A)
B)
C)
D)
E)
. Find the value of s that will make . A)
B)
C)
D)
E)
4
Multiply both sides of the equation by the LCD, and then solve the resulting quadratic equation.
A)
B)
C)
D)
E)
by the LCD, and then solve the resulting quadratic equation. A)
B)
C)
D)
E)
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5
The sensitivity S to a drug is related to the dosage size by , where x is the dosage size in milliliters. Determine all dosages that yield 0 sensitivity.
A) milliliters, milliliters
B) milliliters, milliliters
C) milliliters, milliliters
D) milliliters, milliliters
E) milliliters
, where x is the dosage size in milliliters. Determine all dosages that yield 0 sensitivity. A)
milliliters, millilitersB)
milliliters, millilitersC)
milliliters, millilitersD)
milliliters, millilitersE)
milliliters Unlock Deck
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6
Solve the equation .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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7
Solve the equation by using the quadratic formula. Give real answers rounded to two decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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8
If a ball is thrown upward at 80 feet per second from the top of a building that is 100 feet high, the height of the ball can be modeled by , where t is the number of seconds after the ball is thrown. How long after it is thrown is the height 100 feet?
A) seconds
B) seconds
C) seconds
D) seconds
E) seconds
, where t is the number of seconds after the ball is thrown. How long after it is thrown is the height 100 feet?A)
secondsB)
secondsC)
secondsD)
secondsE)
seconds Unlock Deck
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9
Find the exact real solutions of the equation , if they exist.
A) and
B) and
C) and
D) and
E) Real solutions do not exist.
, if they exist. A)
and B)
and C)
and D)
and E) Real solutions do not exist.
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10
Find the exact real solutions of the equation , if they exist.
A) and
B) and
C) and
D) and
E) and
, if they exist. A)
and B)
and C)
and D)
and E)
and Unlock Deck
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11
Solve the equation by using a graphing utility.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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12
Find the exact real solutions to the equation, if they exist.
A)
B)
C)
D)
E) no real solutions
A)
B)
C)
D)
E) no real solutions
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13
Write the equation in general form.
A)
B)
C)
D)
E)
in general form. A)
B)
C)
D)
E)
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14
Solve the equation by factoring.
A)
B)
C)
D)
E)
by factoring. A)
B)
C)
D)
E)
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15
Solve the equation by using the quadratic formula. Give real solutions only.
A)
B)
C)
D) no real solutions
E)
A)
B)
C)
D) no real solutions
E)
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16
Solve the equation below using quadratic methods.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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17
Solve the equation by first multiplying by the LCD, and then solving the resulting equation.
A)
B)
C)
D)
E)
by first multiplying by the LCD, and then solving the resulting equation. A)
B)
C)
D)
E)
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18
Find the exact real solutions to the equation, if they exist.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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19
If the profit from the sale of x units of a product is , what level(s) of production will yield a profit of $1,000?
A) less 15 units of production.
B) more than 80 units of production.
C) 95 units of production.
D) 65 units of production.
E) 15 or 80 units of production.
, what level(s) of production will yield a profit of $1,000? A) less 15 units of production.
B) more than 80 units of production.
C) 95 units of production.
D) 65 units of production.
E) 15 or 80 units of production.
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20
Solve the equation by using a graphing utility. Round your answers to two decimal places.
A) and
B) and
C) and
D) and
E) and
by using a graphing utility. Round your answers to two decimal places. A)
and B)
and C)
and D)
and E)
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21
Determine whether the function's vertex is a maximum point or a minimum point and find the coordinates of this point.
A) vertex: , a minimum point
B) vertex: , a maximum point
C) vertex: , a minimum point
D) vertex: , a maximum point
E) vertex: , a maximum point
A) vertex:
, a minimum pointB) vertex:
, a maximum pointC) vertex:
, a minimum pointD) vertex:
, a maximum pointE) vertex:
, a maximum point Unlock Deck
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22
Find the average rate of change of the function between the given values of x. between and .
A) 15
B) 50
C) 0
D) -6
E) 100
between and .
A) 15
B) 50
C) 0
D) -6
E) 100
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23
How is the graph of shifted to obtain the graph of the function ?
A) shifted 12 units to the left and 13 units up
B) shifted 12 units to the right and 13 units down
C) shifted 144 units to the left and 13 units up
D) shifted 24 units to the right and 13 units down
E) shifted 12 units to the right and 13 units up
shifted to obtain the graph of the function ? A) shifted 12 units to the left and 13 units up
B) shifted 12 units to the right and 13 units down
C) shifted 144 units to the left and 13 units up
D) shifted 24 units to the right and 13 units down
E) shifted 12 units to the right and 13 units up
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24
Find the vertex of the graph of the equation . Round your answer to two decimal places.
A)
B)
C)
D)
E)
. Round your answer to two decimal places. A)
B)
C)
D)
E)
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25
A fissure in the earth appeared after an earthquake. To measure its vertical depth, a stone was dropped into it, and the sound of the stone's impact was heard 3.3 seconds later. The distance (in feet) the stone fell is given by , and the distance (in feet) the sound traveled is given by . In these equations, the distances traveled by the sound and the stone are the same, but their times are not. Using the fact that the total time is 3.3 seconds, find the depth of the fissure. Round your answer to two decimal places.
A) 94.19 feet
B) 91.00 feet
C) 121.98 feet
D) 126.38 feet
E) 126.48 feet
, and the distance (in feet) the sound traveled is given by . In these equations, the distances traveled by the sound and the stone are the same, but their times are not. Using the fact that the total time is 3.3 seconds, find the depth of the fissure. Round your answer to two decimal places. A) 94.19 feet
B) 91.00 feet
C) 121.98 feet
D) 126.38 feet
E) 126.48 feet
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26
Determine what value of x gives the optimal value of the function, and determine the optimal (maximum or minimum) value. Round your answers to two decimal places.
A) optimal value of x: 0, optimal value: 1.00
B) optimal value of x: -1.13, optimal value: 0.75
C) optimal value of x: 1.50, optimal value: -1.50
D) optimal value of x: -0.75, optimal value: -1.13
E) optimal value of x: 0.75, optimal value: -1.13
A) optimal value of x: 0, optimal value: 1.00
B) optimal value of x: -1.13, optimal value: 0.75
C) optimal value of x: 1.50, optimal value: -1.50
D) optimal value of x: -0.75, optimal value: -1.13
E) optimal value of x: 0.75, optimal value: -1.13
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27
Find the vertex and then determine the range of the function.
A) all values greater than or equal to 67
B) all values less than or equal to 63
C) all values greater than or equal to 10
D) all values less than or equal to 85
E) all values less than or equal to 67
A) all values greater than or equal to 67
B) all values less than or equal to 63
C) all values greater than or equal to 10
D) all values less than or equal to 85
E) all values less than or equal to 67
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28
Sketch the graph of the following function by using graphing calculator.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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29
Find the vertex of the graph of the equation .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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30
Find the zeros, if any exist. Round your answers to two decimal places.
A) zeros at -2.17 and -7.83
B) zeros at 0 and 10.00
C) zeros at 11.00 and -21.00
D) no zeros
E) zeros at 0 and 27.00
A) zeros at -2.17 and -7.83
B) zeros at 0 and 10.00
C) zeros at 11.00 and -21.00
D) no zeros
E) zeros at 0 and 27.00
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31
Find the x-intercepts, if any exist. Round your answers to two decimal places.
A) x-intercepts: ,
B) x-intercepts: ,
C) x-intercepts: ,
D) x-intercepts: ,
E) no x-intercepts
A) x-intercepts:
, B) x-intercepts:
, C) x-intercepts:
, D) x-intercepts:
, E) no x-intercepts
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32
The time t, in seconds, that it takes a 2005 Corvette to accelerate to x mph can be described by . How fast is the Corvette going after 9.08 seconds? Give your answer to the nearest tenth.
A) 97.1 mph
B) 98.1 mph
C) 100.1 mph
D) 118.9 mph
E) 119.4 mph
. How fast is the Corvette going after 9.08 seconds? Give your answer to the nearest tenth. A) 97.1 mph
B) 98.1 mph
C) 100.1 mph
D) 118.9 mph
E) 119.4 mph
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33
Use a graphing utility to approximate the solutions to . Round your answers to two decimal places.
A)
B)
C)
D)
E)
. Round your answers to two decimal places. A)
B)
C)
D)
E)
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34
Determine whether the vertex of the graph of the following function is a maximum point or a minimum point. Also find the coordinates of the vertex.
A) vertex: , a maximum point
B) vertex: , a minimum point
C) vertex: , a minimum point
D) vertex: , a minimum point
E) vertex: , a maximum point
A) vertex:
, a maximum pointB) vertex:
, a minimum pointC) vertex:
, a minimum pointD) vertex:
, a minimum pointE) vertex:
, a maximum point Unlock Deck
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35
Determine if the vertex of the graph of the equation is a maximum or minumim point.
A) vertex is at a maximum point
B) vertex is at a minimum point
C) has no vertex
A) vertex is at a maximum point
B) vertex is at a minimum point
C) has no vertex
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36
Sketch the graph of the following function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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37
Use a graphing utility to find the vertex of the function. Round your answer to two decimal places.
A) vertex:
B) vertex: origin
C) vertex:
D) vertex:
E) vertex:
A) vertex:
B) vertex: origin
C) vertex:
D) vertex:
E) vertex:
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38
Suppose that the percent of total personal income that is used to pay personal taxes is given by , where x is the number of years past 1990 (Source: Bureau of Economic Analysis, U.S. Department of Commerce). Find the year or years when the percent of total personal income used to pay personal taxes is 18 percent.
A) 2013
B) 2003
C) 2002
D) 2008
E) 2044
, where x is the number of years past 1990 (Source: Bureau of Economic Analysis, U.S. Department of Commerce). Find the year or years when the percent of total personal income used to pay personal taxes is 18 percent. A) 2013
B) 2003
C) 2002
D) 2008
E) 2044
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39
An equation that models the number of users of the Internet is million users, where x is the number of years past 1990 (Source: CyberAtlas, 1999). If the pattern indicated by the model remains valid, when does this model predict there will be 1,100 million users?
A) 2004
B) 2021
C) 2014
D) 2007
E) 2005
million users, where x is the number of years past 1990 (Source: CyberAtlas, 1999). If the pattern indicated by the model remains valid, when does this model predict there will be 1,100 million users? A) 2004
B) 2021
C) 2014
D) 2007
E) 2005
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40
The model for body-heat loss depends on the coefficient of convection K, which depends on wind speed v according to the equation where v is in miles per hour. Find the positive coefficient of convection when the wind speed is 29 mph. Round your answer to the nearest integer.
A)
B)
C)
D)
E)
where v is in miles per hour. Find the positive coefficient of convection when the wind speed is 29 mph. Round your answer to the nearest integer. A)
B)
C)
D)
E)
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41
The daily profit from the sale of a product is given by dollars. What is the maximum possible profit? Round intermediate calculations and final answer to the nearest dollar.
A) $1,701
B) $2,613
C) $808
D) $95
E) $185
dollars. What is the maximum possible profit? Round intermediate calculations and final answer to the nearest dollar. A) $1,701
B) $2,613
C) $808
D) $95
E) $185
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42
The supply function for a product is , while the demand function for the same product is . Find the market equilibrium point E(q, p). Round your final answer to two decimal places.
A)
B)
C)
D)
E)
, while the demand function for the same product is . Find the market equilibrium point E(q, p). Round your final answer to two decimal places. A)
B)
C)
D)
E)
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43
If the supply function for a commodity is and the demand function is , find the equilibrium quantity and equilibrium price. Round your final answer to two decimal places.
A)
B)
C)
D)
E)
and the demand function is , find the equilibrium quantity and equilibrium price. Round your final answer to two decimal places. A)
B)
C)
D)
E)
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44
When a stone is thrown upward, it follows a parabolic path given by a form of the equation . If represents ground level, find the equation of a stone that is thrown from ground level at and lands on the ground 130 units away if the stone reaches a maximum height of 130 units.
A)
B)
C)
D)
E)
. If represents ground level, find the equation of a stone that is thrown from ground level at and lands on the ground 130 units away if the stone reaches a maximum height of 130 units. A)
B)
C)
D)
E)
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45
Sketch the first quadrant portions of the following functions and estimate the market equilibrium point.
Supply: Demand:
A)
B)
C)
D)
E)
Supply:
Demand: A)
B)
C)
D)
E)
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46
In 1995, America's 45 million Social Security recipients received a 2.6% cost-of-living increase, the second smallest increase in nearly 20 years, a reflection of lower inflation. The percent increase might be described by the function , where t is the number of years past 1980. In what year does the model predict the highest cost of living percent increase?
A) 1990
B) 2009
C) 1987
D) 1989
E) none of the above
, where t is the number of years past 1980. In what year does the model predict the highest cost of living percent increase? A) 1990
B) 2009
C) 1987
D) 1989
E) none of the above
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47
If the supply and demand functions for a commodity are given by and , what is the equilibrium price and what is the corresponding number of units supplied and demanded? Round your answer to two decimal places.
A)
B)
C)
D)
E)
and , what is the equilibrium price and what is the corresponding number of units supplied and demanded? Round your answer to two decimal places. A)
B)
C)
D)
E)
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48
A ball thrown vertically into the air has its height above ground given by , where t is in seconds and s is in feet. Find the maximum height of the ball.
A) 242 feet
B) 121 feet
C) 8 feet
D) 16 feet
E) 229 feet
, where t is in seconds and s is in feet. Find the maximum height of the ball. A) 242 feet
B) 121 feet
C) 8 feet
D) 16 feet
E) 229 feet
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49
The owner of a skating rink rents the rink for parties at $912 if 76 or fewer skaters attend, so that the cost per person is $12 if 76 attend. For each 5 skaters above 76, she reduces the price per skater by $0.50. Which table gives the revenue generated if 76, 86, and 96 skaters attend?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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50
The daily profit from the sale of a product is given by dollars. What level of production maximizes profit?
A) production level of 100 units
B) production level of 10 units
C) production level of 5 units
D) production level of 50 units
E) production level of 95 units
dollars. What level of production maximizes profit? A) production level of 100 units
B) production level of 10 units
C) production level of 5 units
D) production level of 50 units
E) production level of 95 units
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51
If a firm has the following cost and revenue functions, find the break-even points.
A) Break-even values are at and units.
B) Break-even values are at and units.
C) Break-even values are at and units.
D) Break-even values are at and units.
E) Break-even values are at and units.
A) Break-even values are at
and units.B) Break-even values are at
and units.C) Break-even values are at
and units.D) Break-even values are at
and units.E) Break-even values are at
and units. Unlock Deck
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52
The supply function for a product is , while the demand function for the same product is . If a $22 tax is placed on production of the item, then the supplier passes this tax on by adding $22 to his selling price. Find the new equilibrium point E(q, p) for this product when the tax is passed on. (The new supply function is given by .) Round your final answer to two decimal places.
A)
B)
C)
D)
E)
, while the demand function for the same product is . If a $22 tax is placed on production of the item, then the supplier passes this tax on by adding $22 to his selling price. Find the new equilibrium point E(q, p) for this product when the tax is passed on. (The new supply function is given by .) Round your final answer to two decimal places. A)
B)
C)
D)
E)
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53
If the supply and demand functions for a commodity are given by and , respectively, find the price that will result in market equilibrium.
A) 41
B) 150
C) 33
D) 31
E) 25
and , respectively, find the price that will result in market equilibrium. A) 41
B) 150
C) 33
D) 31
E) 25
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54
The yield in bushels from a grove of orange trees is given by , where x is the number of orange trees per acre. How many trees will maximize the yield?
A) 1,500 trees
B) 3,000 trees
C) 800 trees
D) 1,550 trees
E) 750 trees
, where x is the number of orange trees per acre. How many trees will maximize the yield? A) 1,500 trees
B) 3,000 trees
C) 800 trees
D) 1,550 trees
E) 750 trees
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55
The total costs for a company are given by , and the total revenues are given by . Find the break-even points.
A) Break-even values are at x = 35 and x = 70 units.
B) Break-even values are at x = inf units.
C) Break-even values are at x = -inf units.
D) Break-even values are at x = 17.5 and x = 35 units.
E) Break-even values are at x = 70 units.
, and the total revenues are given by . Find the break-even points. A) Break-even values are at x = 35 and x = 70 units.
B) Break-even values are at x = inf units.
C) Break-even values are at x = -inf units.
D) Break-even values are at x = 17.5 and x = 35 units.
E) Break-even values are at x = 70 units.
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56
The sensitivity S to a drug is related to the dosage x in milligrams by . Use a graphing utility to determine what dosage gives maximum sensitivity.
A) 97
B) 235,225
C) 970, 0
D) 970
E) 485
. Use a graphing utility to determine what dosage gives maximum sensitivity. A) 97
B) 235,225
C) 970, 0
D) 970
E) 485
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57
A supply function has the equation is , and the demand function is decribed by the equation . Algebraically determine the equilibrium point for the supply and demand functions. Round your answer to two decimal places.
A)
B)
C)
D)
E)
, and the demand function is decribed by the equation . Algebraically determine the equilibrium point for the supply and demand functions. Round your answer to two decimal places. A)
B)
C)
D)
E)
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58
Solve for the function .
A)
B)
C)
D)
E) no real solutions
for the function . A)
B)
C)
D)
E) no real solutions
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59
Factor the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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60
The daily profit from the sale of a product is given by dollars. What is the maximum possible profit? Round intermediate calculations and final answer to the nearest dollar.
A) $5,423
B) $16,685
C) $11,013
D) $137
E) $271
dollars. What is the maximum possible profit? Round intermediate calculations and final answer to the nearest dollar. A) $5,423
B) $16,685
C) $11,013
D) $137
E) $271
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61
Suppose a company has fixed costs of $27,000 and variable costs of dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is dollars per unit. Find the maximum revenue. Round your answer to the nearest cent.
A) Maximum revenue is $1,026.70.
B) Maximum revenue is $27,000.00.
C) Maximum revenue is $26,862.50.
D) Maximum revenue is $677,343.75.
E) Maximum revenue is $612.50.
dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is dollars per unit. Find the maximum revenue. Round your answer to the nearest cent. A) Maximum revenue is $1,026.70.
B) Maximum revenue is $27,000.00.
C) Maximum revenue is $26,862.50.
D) Maximum revenue is $677,343.75.
E) Maximum revenue is $612.50.
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62
Sketch the graph of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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63
Assume that sales revenues, in millions, for Continental Divide Mining can be described by , where t is the number of years past 1992. Use the function to find the maximum revenue. Round your answers to three decimal places.
A) Maximum revenue is $9.463 million.
B) Maximum revenue is $5.971 million.
C) Maximum revenue is $3.672 million.
D) Maximum revenue is $3.851 million.
E) Maximum revenue is $16.986 million.
, where t is the number of years past 1992. Use the function to find the maximum revenue. Round your answers to three decimal places. A) Maximum revenue is $9.463 million.
B) Maximum revenue is $5.971 million.
C) Maximum revenue is $3.672 million.
D) Maximum revenue is $3.851 million.
E) Maximum revenue is $16.986 million.
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64
Form the profit function for the cost and revenue functions, where the total costs and total revenues are given by and .
A)
B)
C)
D)
E)
and . A)
B)
C)
D)
E)
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65
The graph of the profit function is given as follows. Consider the average rate of change of the profit from a to 400 where a lies to the left of 400. Does the average rate of change of the profit get closer to 0 or farther from 0 as a gets closer to 400?
A) closer to 0
B) farther from 0
is given as follows. Consider the average rate of change of the profit from a to 400 where a lies to the left of 400. Does the average rate of change of the profit get closer to 0 or farther from 0 as a gets closer to 400? A) closer to 0
B) farther from 0
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66
If, in a monopoly market, the demand for a product is , and the revenue function is , where x is the number of units sold, what price will maximize revenue? Round your answer to the nearest cent.
A) Price that will maximize revenue is .
B) Price that will maximize revenue is .
C) Price that will maximize revenue is .
D) Price that will maximize revenue is .
E) Price that will maximize revenue is .
, and the revenue function is , where x is the number of units sold, what price will maximize revenue? Round your answer to the nearest cent. A) Price that will maximize revenue is
.B) Price that will maximize revenue is
.C) Price that will maximize revenue is
.D) Price that will maximize revenue is
.E) Price that will maximize revenue is
. Unlock Deck
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67
Sketch the graph of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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68
Given the profit function, , and that production is restricted to fewer than 75 units, find the break-even point(s). Round your answer to two decimal places.
A) Break-even value is at units.
B) Break-even value is at units.
C) Break-even value is at units.
D) Break-even value is at units.
E) Break-even value is at units.
, and that production is restricted to fewer than 75 units, find the break-even point(s). Round your answer to two decimal places. A) Break-even value is at
units.B) Break-even value is at
units.C) Break-even value is at
units.D) Break-even value is at
units.E) Break-even value is at
units. Unlock Deck
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69
Find the maximum revenue for the revenue function . Round your answer to the nearest cent.
A) $84,008.93
B) $252,026.79
C) $48,005.10
D) $216,022.96
E) $253,026.79
. Round your answer to the nearest cent. A) $84,008.93
B) $252,026.79
C) $48,005.10
D) $216,022.96
E) $253,026.79
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70
Use a graphing calculator to graph the profit function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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71
If a company has total costs , and total revenues given by , find the break-even points. Round your answers to two decimal places.
A) Break-even values are at and units.
B) Break-even values are at and units.
C) Break-even values are at and units.
D) Break-even values are at units.
E) Break-even values are at and units.
, and total revenues given by , find the break-even points. Round your answers to two decimal places. A) Break-even values are at
and units.B) Break-even values are at
and units.C) Break-even values are at
and units.D) Break-even values are at
units.E) Break-even values are at
and units. Unlock Deck
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Unlock Deck
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72
If total costs are and total revenues are , find the break-even points.
A) Break-even values are at and units.
B) Break-even values are at and units.
C) Break-even values are at and units.
D) Break-even values are at and units.
E) Break-even values are at and units.
and total revenues are , find the break-even points. A) Break-even values are at
and units.B) Break-even values are at
and units.C) Break-even values are at
and units.D) Break-even values are at
and units.E) Break-even values are at
and units. Unlock Deck
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Unlock Deck
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73
The profit function for a certain commodity is . Find the level of production that yields maximum profit, and find the maximum profit.
A) Production levels of 110 yields a maximum profit of $1,200.
B) Production levels of 110 yields a maximum profit of $1,825.
C) Production levels of 55 yields a maximum profit of $4,795.
D) Production levels of 55 yields a maximum profit of $3,025.
E) Production levels of 55 yields a maximum profit of $1,825.
. Find the level of production that yields maximum profit, and find the maximum profit. A) Production levels of 110 yields a maximum profit of $1,200.
B) Production levels of 110 yields a maximum profit of $1,825.
C) Production levels of 55 yields a maximum profit of $4,795.
D) Production levels of 55 yields a maximum profit of $3,025.
E) Production levels of 55 yields a maximum profit of $1,825.
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74
Sketch the graph of the function below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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75
Sketch the graph of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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76
Suppose a company has fixed costs of $26,000 and variable costs of dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is dollars per unit. Find the break-even points. Round your answer to the nearest cent.
A) Break-even values are at and .
B) Break-even values are at and .
C) Break-even values are at and .
D) Break-even values are at and .
E) Break-even values are at and .
dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is dollars per unit. Find the break-even points. Round your answer to the nearest cent. A) Break-even values are at
and .B) Break-even values are at
and .C) Break-even values are at
and .D) Break-even values are at
and .E) Break-even values are at
and . Unlock Deck
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77
Assume that sales revenues for Continental Divide Mining can be described by , where t is the number of years past 1992. Use the function to determine the year in which maximum revenue occurs.
A) Maximum revenue occurred during 1998.
B) Maximum revenue occurred during 1992.
C) Maximum revenue occurred during 1997.
D) Maximum revenue occurred during 2003.
E) Maximum revenue occurred during 1991.
, where t is the number of years past 1992. Use the function to determine the year in which maximum revenue occurs. A) Maximum revenue occurred during 1998.
B) Maximum revenue occurred during 1992.
C) Maximum revenue occurred during 1997.
D) Maximum revenue occurred during 2003.
E) Maximum revenue occurred during 1991.
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78
Assume that costs and expenses for Continental Divide Mining can be described by and the sales revenue can be described by , where t is the number of years since the beginning of 1992. Find the year in which maximum profit occurs.
A) 2014
B) 1993
C) 2003
D) 2004
E) 1994
and the sales revenue can be described by , where t is the number of years since the beginning of 1992. Find the year in which maximum profit occurs. A) 2014
B) 1993
C) 2003
D) 2004
E) 1994
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79
Sketch the graph of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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80
Sketch the graph of the function .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Unlock Deck
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Unlock Deck
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