Question 1

Find

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    E

Question 2

Given the units of measure for production and the units of measure for cost or revenue. Write a sentence interpreting the marginal as an increase. Revenue is given by   hundred dollars when q thousand units are sold;   .

Accepted Answer

A)  When 16 thousand units are sold, revenue is increasing by $0.30 per unit. 
B)  When 16 thousand units are sold, revenue is decreasing by $0.30 per unit. 
C)  When 16 thousand units are sold, revenue is increasing by $30 per unit. 
D)  When 16 thousand units are sold, revenue is decreasing by $30 per unit. 
E)  When 16 thousand units are sold, revenue is increasing by $3 per unit. 
A)  When 16 thousand units are sold, revenue is increasing by $0.30 per unit. 
B)  When 16 thousand units are sold, revenue is decreasing by $0.30 per unit. 
C)  When 16 thousand units are sold, revenue is increasing by $30 per unit. 
D)  When 16 thousand units are sold, revenue is decreasing by $30 per unit. 
E)  When 16 thousand units are sold, revenue is increasing by $3 per unit. A

Question 3

Find   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)    A

Question 4

The future value of an investment after t years is given by   thousand dollars. Use the linearization to estimate the future value after 10.5 years.

Accepted Answer

A)  $ 416.484 thousand dollars 
B)  $ 49.508 thousand dollars 
C)  $ 32.419 thousand dollars 
D)  $ 21.501 thousand dollars 
E)  $ 216.734 thousand dollars 
A)  $ 416.484 thousand dollars 
B)  $ 49.508 thousand dollars 
C)  $ 32.419 thousand dollars 
D)  $ 21.501 thousand dollars 
E)  $ 216.734 thousand dollars

Question 5

The population of a certain region between 1790 and 2000 can be modeled by   thousand people x years after 1790. Use the rate of change of the population of the region in 2000 to estimate, to the nearest thousand, the population in 2003.

Accepted Answer

A)  3,655,000 people 
B)  4,000 people 
C)  5,326,000 people 
D)  3,797,000 people 
E)  3,653,000 people 
A)  3,655,000 people 
B)  4,000 people 
C)  5,326,000 people 
D)  3,797,000 people 
E)  3,653,000 people

Question 6

A street vendor constructs the table below on the basis of sales data. Construct a model for consumer expenditure (revenue for the vendor). Sales of Roses, Given the Price per Dozen

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

Find the first and second derivatives of the function.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

The table lists the time in seconds that an average athlete takes to swim 100 meters freestyle at age x years. Find a model for the data. Time That an Average Athlete Takes to Swim 100 Meters
Freestyle

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 9

The population of a certain region between 1790 and 2000 can be modeled by   thousand people x years after 1790. Find the rate of change of the population of the region in 2000 to the nearest thousand people per year.

Accepted Answer

A)  4,771 thousand people per year 
B)  21 thousand people per year 
C)  988 thousand people per year 
D)  30 thousand people per year 
E)  65 thousand people per year 
A)  4,771 thousand people per year 
B)  21 thousand people per year 
C)  988 thousand people per year 
D)  30 thousand people per year 
E)  65 thousand people per year

Question 10

Boyle's law for enclosed gases states that at a constant temperature, the pressure is related to the volume by the equation   , where k is a constant. If the volume is increasing at a rate of 8 cubic inches per hour, at what rate is the pressure changing when the volume is 40 cubic inches and   inch-pounds?

Accepted Answer

A)  0.003 lb/in2/hr 
B)  -0.003 lb/in2/hr 
C)  -12.800 lb/in2/hr 
D)  1.000 lb/in2/hr 
E)  -0.025 lb/in2/hr 
A)  0.003 lb/in2/hr 
B)  -0.003 lb/in2/hr 
C)  -12.800 lb/in2/hr 
D)  1.000 lb/in2/hr 
E)  -0.025 lb/in2/hr

Question 11

A tin-container manufacturing company uses the same machine to produce different items such as popcorn tins and 30-gallon storage drums. The machine is set up to produce a quantity of one item and then is reconfigured to produce a quantity of another item. The plant produces a run and then ships the tins out at a constant rate so that the warehouse is empty for storing the next run. Assume that the number of tins stored on average during 1 year is half of the number of tins produced in each run. A plant manager must take into account the cost to reset the machine and the cost to store inventory. Although it might otherwise make sense to produce an entire year's inventory of popcorn tins at once, the cost of storing all the tins over a year's time would be prohibitive. Suppose the company needs to produce 1.7 million popcorn tins over the course of a year. The cost to set up the machine for production is $1300, and the cost to store one tin for a year is approximately $1. What size production run will minimize setup and storage costs?

Accepted Answer

A)  66,483 cans 
B)  53,403 cans 
C)  76,453 cans 
D)  46,473 cans 
E)  56,423 cans 
A)  66,483 cans 
B)  53,403 cans 
C)  76,453 cans 
D)  46,473 cans 
E)  56,423 cans

Question 12

Find the second derivative of the function   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

Assume that s, r, and h are differentiable functions of t. If   , find   when

Accepted Answer

A)  -0.20 
B)  1.08 
C)  2.33 
D)  -0.33 
E)  1.40 
A)  -0.20 
B)  1.08 
C)  2.33 
D)  -0.33 
E)  1.40

Question 14

Suppose the flow rate (in cubic feet per second, cfs) of a river in the first 11 hours after the beginning of a severe thunderstorm can be modeled as   cfs where h is the number of hours after the storm began. What are the flow rates for   and   ?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Find the derivative of the function.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Find the first and second derivatives of the function.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

Differentiate the given function with respect to t where r is the radius, and A is the area of the circle. Then, evaluate   with

Accepted Answer

A)  49   
B)  56   
C)  16   
D)  14   
E)  112   
A)  49   
B)  56   
C)  16   
D)  14   
E)  112

Question 18

Find all relative maxima of the given function.

Accepted Answer

A)    
B)    
C)    
D)    ,   
E)  no relative maxima 
A)    
B)    
C)    
D)    ,   
E)  no relative maxima

Question 19

Find the derivative.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 20

The humidity is currently 32% and falling at a rate of 4 percentage points per hour. Estimate the change in humidity over the next 20 minutes.

Accepted Answer

A)    percentage points 
B)    percentage points 
C)    percentage points 
D)    percentage points 
E)    percentage points 
A)    percentage points 
B)    percentage points 
C)    percentage points 
D)    percentage points 
E)    percentage points

Find

Given the units of measure for production and the units of measure for cost or revenue. Write a sentence interpreting the marginal as an increase. Revenue is given by hundred dollars when q thousand units are sold; .

Find .

The future value of an investment after t years is given by thousand dollars. Use the linearization to estimate the future value after 10.5 years.

The population of a certain region between 1790 and 2000 can be modeled by thousand people x years after 1790. Use the rate of change of the population of the region in 2000 to estimate, to the nearest thousand, the population in 2003.

A street vendor constructs the table below on the basis of sales data. Construct a model for consumer expenditure (revenue for the vendor). Sales of Roses, Given the Price per Dozen

Find the first and second derivatives of the function.

The table lists the time in seconds that an average athlete takes to swim 100 meters freestyle at age x years. Find a model for the data. Time That an Average Athlete Takes to Swim 100 Meters Freestyle

The population of a certain region between 1790 and 2000 can be modeled by thousand people x years after 1790. Find the rate of change of the population of the region in 2000 to the nearest thousand people per year.

Find the second derivative of the function .

Assume that s, r, and h are differentiable functions of t. If , find when

Suppose the flow rate (in cubic feet per second, cfs) of a river in the first 11 hours after the beginning of a severe thunderstorm can be modeled as cfs where h is the number of hours after the storm began. What are the flow rates for and ?

Find the derivative of the function.

Find the first and second derivatives of the function.

Differentiate the given function with respect to t where r is the radius, and A is the area of the circle. Then, evaluate with

Find all relative maxima of the given function.

Find the derivative.

The humidity is currently 32% and falling at a rate of 4 percentage points per hour. Estimate the change in humidity over the next 20 minutes.

Ingredients of Change: Functions an Limits

Describing Change: Rates

Determining Change: Derivatives

Accumulating Change: Limits of Sums and the Definite Integral

Analyzing Accumulated Change: Integrals in Action

Ingredients of Multivariable Change: Models, Graphs, Rates

Analyzing Multivariable Change: Optimization

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Exam 4: Analyzing Change: Applications of Derivatives

Find

Given the units of measure for production and the units of measure for cost or revenue. Write a sentence interpreting the marginal as an increase. Revenue is given by hundred dollars when q thousand units are sold; .

Find .

The future value of an investment after t years is given by thousand dollars. Use the linearization to estimate the future value after 10.5 years.

The population of a certain region between 1790 and 2000 can be modeled by thousand people x years after 1790. Use the rate of change of the population of the region in 2000 to estimate, to the nearest thousand, the population in 2003.

A street vendor constructs the table below on the basis of sales data. Construct a model for consumer expenditure (revenue for the vendor). Sales of Roses, Given the Price per Dozen

Find the first and second derivatives of the function.

The table lists the time in seconds that an average athlete takes to swim 100 meters freestyle at age x years. Find a model for the data. Time That an Average Athlete Takes to Swim 100 Meters Freestyle

The population of a certain region between 1790 and 2000 can be modeled by thousand people x years after 1790. Find the rate of change of the population of the region in 2000 to the nearest thousand people per year.

Find the second derivative of the function .

Assume that s, r, and h are differentiable functions of t. If , find when

Suppose the flow rate (in cubic feet per second, cfs) of a river in the first 11 hours after the beginning of a severe thunderstorm can be modeled as cfs where h is the number of hours after the storm began. What are the flow rates for and ?

Find the derivative of the function.

Find the first and second derivatives of the function.

Differentiate the given function with respect to t where r is the radius, and A is the area of the circle. Then, evaluate with

Find all relative maxima of the given function.

Find the derivative.

The humidity is currently 32% and falling at a rate of 4 percentage points per hour. Estimate the change in humidity over the next 20 minutes.

Ingredients of Change: Functions an Limits

Describing Change: Rates

Determining Change: Derivatives

Accumulating Change: Limits of Sums and the Definite Integral

Analyzing Accumulated Change: Integrals in Action

Ingredients of Multivariable Change: Models, Graphs, Rates

Analyzing Multivariable Change: Optimization

Filters