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Deck 13: Indefinite Integrals
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Question
Evaluate the integral 
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Evaluate the integral 
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Question
If the marginal revenue (in dollars per unit) for a month is given by 
, find the total revenue from the sale of 125 units to the nearest cent.
A)$5,194.29
B)$5,193.11
C)$5,195.31
D)$41.13
E)$39.93
, find the total revenue from the sale of 125 units to the nearest cent. A)$5,194.29
B)$5,193.11
C)$5,195.31
D)$41.13
E)$39.93
Question
Find a function g(x) such that 
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Suppose that a particle has been shot into the air in such a way that the rate at which its height H (in feet per second) is changing is 
. If the particle is 4,200 feet high when 
seconds, write the formula for the height of the particle at any time t.
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. If the particle is 4,200 feet high when seconds, write the formula for the height of the particle at any time t.A)
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Evaluate the integral 
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Evaluate the integral 
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Evaluate the integral 
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Evaluate the integral 
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Question
The DeWitt Company has found that the rate of change of its average cost of producing a product is 
, where x is the number of units and cost is in dollars. The average cost of producing 20 units is $40.00. Find the average cost of producing 140 units of the product. Round to the nearest dollar.
A)$46
B)$48
C)$51
D)$53
E)$58
, where x is the number of units and cost is in dollars. The average cost of producing 20 units is $40.00. Find the average cost of producing 140 units of the product. Round to the nearest dollar. A)$46
B)$48
C)$51
D)$53
E)$58
Question
Evaluate the integral 
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Evaluate the integral 
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Use algebra to rewrite the integrand; then integrate and simplify. 
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Evaluate the integral 
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Question
Suppose that when a sense organ receives a stimulus at time t, the total number of action potentials is P(t). If the rate at which action potentials are produced is 
, and if there are 0 action potentials when 
, find the formula for P(t).
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B)
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, and if there are 0 action potentials when , find the formula for P(t). A)
B)
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E)
Question
If 
, find 
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, find . A)
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Evaluate the integral 
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Evaluate the integral 
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A family of functions is given and the graph of some members of the family are shown. Write the indefinite integral that gives the family. 
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Evaluate the integral 
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Evaluate the integral 
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Evaluate the integral 
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Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2). 
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Evaluate the integral 
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Find du if 
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Evaluate the integral 
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Evaluate the integral 
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Question
Suppose an oil tanker hits a reef and begins to leak. The efforts of the workers repairing the leak cause the rate at which the oil is leaking to decrease. The oil was leaking at a rate of 41 barrels per hour at the end of the first hour after the accident, and the rate is decreasing at a rate of one barrel per hour. What formula describes the rate of loss in terms of the time t that has lapsed since the leak began?
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Question
The total physical output of a number of machines or workers is called physical productivity and is a function of the number of machines or workers. If 
is the productivity, 
is the marginal physical productivity. If the marginal physical productivity for bricklayers is 
, where P is the number of bricks laid per day and x is the number of bricklayers, find the physical productivity of 5 bricklayers. (Note: 
when 
.)
A)88,330 bricks laid per day
B)719,114 bricks laid per day
C)715,550 bricks laid per day
D)68,255 bricks laid per day
E)552,925 bricks laid per day
is the productivity, is the marginal physical productivity. If the marginal physical productivity for bricklayers is , where P is the number of bricks laid per day and x is the number of bricklayers, find the physical productivity of 5 bricklayers. (Note: when .) A)88,330 bricks laid per day
B)719,114 bricks laid per day
C)715,550 bricks laid per day
D)68,255 bricks laid per day
E)552,925 bricks laid per day
Question
The marginal revenue for a new calculator is given by 
, where x represents hundreds of calculators and revenue is in dollars. Find the total revenue function for these calculators.
A)
B)
C)
D)
E)
, where x represents hundreds of calculators and revenue is in dollars. Find the total revenue function for these calculators. A)
B)
C)
D)
E)
Question
Evaluate the integral 
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Evaluate the integral 
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Evaluate the integral 
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Evaluate the integral 
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Question
Which of the following integrals cannot be integrated by using the methods studied so far?
(a)
(b)
(c)
(d)
(e)
A)a, b
B)a, b, e
C)b, c, e
D)c, d
E)d, e
(a)
(b)
(c)
(d)
(e)
A)a, b
B)a, b, e
C)b, c, e
D)c, d
E)d, e
Question
Evaluate the integral 
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Evaluate the integral 
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Question
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Write the indefinite integral that gives the family associated with 
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If 
, find 
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, find . A)
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Question
Because of job outsourcing, a western Pennsylvania town predicts that its public school population will decrease at the rate 
, where x is the number of years and N is the total school population. If N = 7,800 when x = 0, what population size is expected in 6 years? Round your answer to nearest integer when applicable.
A)6,376 students
B)7,538 students
C)8,438 students
D)7,276 students
E)9,600 students
, where x is the number of years and N is the total school population. If N = 7,800 when x = 0, what population size is expected in 6 years? Round your answer to nearest integer when applicable. A)6,376 students
B)7,538 students
C)8,438 students
D)7,276 students
E)9,600 students
Question
The rate of production of a new line of products is given by 
, where x is the number of items and t is the number of weeks the product has been in production. Assuming that 
when 
, find out the number of items produced in the fifth week. Round your answer to the nearest whole number.
A)98 items are produced during the fifth week
B)253 items are produced during the fifth week
C)2,083 items are produced during the fifth week
D)55,491 items are produced during the fifth week
E)258 items are produced during the fifth week
, where x is the number of items and t is the number of weeks the product has been in production. Assuming that when , find out the number of items produced in the fifth week. Round your answer to the nearest whole number. A)98 items are produced during the fifth week
B)253 items are produced during the fifth week
C)2,083 items are produced during the fifth week
D)55,491 items are produced during the fifth week
E)258 items are produced during the fifth week
Question
Evaluate the integral 
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Evaluate the integral 
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Evaluate the integral 
. If it's necessary, round your calculations to one decimal place.
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. If it's necessary, round your calculations to one decimal place. A)
B)
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D)
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Question
Evaluate the integral 
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Question
A new fast-food firm predicts that the number of franchises for its products will grow at the rate 
, where t is the number of years. If there is one franchise 
at present 
, how many franchises are predicted for 26 years from now?
A)2,146
B)2,176
C)2,161
D)2,314
E)2,110
, where t is the number of years. If there is one franchise at present , how many franchises are predicted for 26 years from now? A)2,146
B)2,176
C)2,161
D)2,314
E)2,110
Question
Evaluate the integral 
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Question
The rate of production of a new line of products is given by 
, where x is the number of items produced and t is the number of weeks the product has been in production. Assuming that 
when 
, find the total number of items produced as a function of time t.
A)
B)
C)
D)
E)
, where x is the number of items produced and t is the number of weeks the product has been in production. Assuming that when , find the total number of items produced as a function of time t. A)
B)
C)
D)
E)
Question
Suppose the rate of change of the interest paid on the public debt of the United States as a percent of federal expenditures can be modeled by 
, where t is the number of years past 1930. Use integration and the fact that in 1975, the interest paid as a percent of Federal Expenditures was 12.7, to find the function D(t) that models the interest paid on the public debt of the United States as a percent of federal expenditures. If it's necessary, round your calculations to three decimal places.
A)
B)
C)
D)
E)
, where t is the number of years past 1930. Use integration and the fact that in 1975, the interest paid as a percent of Federal Expenditures was 12.7, to find the function D(t) that models the interest paid on the public debt of the United States as a percent of federal expenditures. If it's necessary, round your calculations to three decimal places. A)
B)
C)
D)
E)
Question
Because a new employee must learn an assigned task, the employee's production will increase with time. Suppose that for the average new employee, the rate of performance is given by 
, where N is the number of units completed t hours after beginning a new task. If 3 units are completed after 8 hours, how many units are completed after 80 hours?
A)8
B)9
C)10
D)12
E)13
, where N is the number of units completed t hours after beginning a new task. If 3 units are completed after 8 hours, how many units are completed after 80 hours? A)8
B)9
C)10
D)12
E)13
Question
Evaluate the integral 
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Question
An inferior product with a large advertising budget does well when it is introduced, but sales decline as people discontinue use of the product. Suppose that the rate of weekly sales revenue is given by 
, where S is the sales in thousands of dollars and t is the time in weeks. Find the function that describes the weekly sales revenue if 
thousand dollars when 
.
A)
B)
C)
D)
E)
, where S is the sales in thousands of dollars and t is the time in weeks. Find the function that describes the weekly sales revenue if thousand dollars when . A)
B)
C)
D)
E)
Question
Given the functions below, decide which function is f (x), and which is a member of the family 
. 
A)
And
Is a member of the family of
B)
And
Is a member of the family of
C)
And
Is a member of the family of
D)
And
Is a member of the family of
E)
And
Is a member of the family of
. A)
And
Is a member of the family of
B)
And
Is a member of the family of
C)
And
Is a member of the family of
D)
And
Is a member of the family of
E)
And
Is a member of the family of
Question
Evaluate the integral 
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Evaluate the integral 
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Evaluate the integral 
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Evaluate the integral 
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Evaluate the integral 
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Evaluate the integral 
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Question
If the marginal cost for a product is 
, and the production of 11 units results in a total cost of $687, find the total cost function C.
A)
B)
C)
D)
E)
, and the production of 11 units results in a total cost of $687, find the total cost function C.A)
B)
C)
D)
E)
Question
Suppose the rate of change of the expected life span l at birth of people born in the United States can be modeled by 
where t is the number of years past 1920. Use integration and the data point for 2007, to find the function that models the life span. If it's necessary, round your calculations to three decimal places, 
A)
B)
C)
D)
E)
where t is the number of years past 1920. Use integration and the data point for 2007, to find the function that models the life span. If it's necessary, round your calculations to three decimal places, A)
B)
C)
D)
E)
Question
A certain firm's marginal cost for a product is 
, its marginal revenue is 
, and its total cost of production of 10 units is $530. Find the optimal level of production.
A)17 units
B)13 units
C)14 units
D)16 units
E)15 units
, its marginal revenue is , and its total cost of production of 10 units is $530. Find the optimal level of production. A)17 units
B)13 units
C)14 units
D)16 units
E)15 units
Question
If $P is invested for n years at 51% compounded continuously, the rate at which the future value is growing is 
. What function describes the future value at the end of n years? Round your answer to two decimal places, if necessary.
A)
B)
C)
D)
E)
. What function describes the future value at the end of n years? Round your answer to two decimal places, if necessary. A)
B)
C)
D)
E)
Question
A store finds that its sales decline after the end of an advertising campaign, with its daily sales for the period declining at the rate 
, where t is the number of days since the end of the campaign. Suppose that 
units when 
. About how many sales should the store expect 17 days after the end of the advertising campaign? Round your answer to the nearest whole number.
A)6,667 sales
B)6,672 sales
C)6,677 sales
D)6,670 sales
E)6,679 sales
, where t is the number of days since the end of the campaign. Suppose that units when . About how many sales should the store expect 17 days after the end of the advertising campaign? Round your answer to the nearest whole number. A)6,667 sales
B)6,672 sales
C)6,677 sales
D)6,670 sales
E)6,679 sales
Question
Suppose the rate of change of total personal income I in the United States (in billions of dollars) can be modeled by 
, where t is the number of years past 1960. Find the total personal income in 2016 by using the arbitrary constant that is evaluated by using the data point from 1960. Also find the rate of change of total personal income in 2016. Round your answers to two decimal places. 
A)
B)
C)
D)
E)
, where t is the number of years past 1960. Find the total personal income in 2016 by using the arbitrary constant that is evaluated by using the data point from 1960. Also find the rate of change of total personal income in 2016. Round your answers to two decimal places. A)
B)
C)
D)
E)
Question
A function f (x) is given below. Find the graph of the member of the family 
that satisfies 
. 
A)
B)
C)
D)
E)
that satisfies . A)
B)
C)
D)
E)
Question
Suppose the rate of change of total personal income I in the United States (in billions of dollars) can be modeled by 
, where t is the number of years past 1960. The value of 
are approximately $19,312.13 and $1,162.81 respectively which are been evaluated by using the arbitrary constant that is been evaluated by using the data point from 1960. Interpret 
. Round your answer to two decimal places, if necessary. 
A)
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be decreasing at a rate of $1,162.81 billion per year.
B)
Means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be increasing at a rate of $19,312.13 billion per year.
C)
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per year.
D)
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per month.
E)
Means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be decreasing at a rate of $19,312.135 billion per month.
, where t is the number of years past 1960. The value of are approximately $19,312.13 and $1,162.81 respectively which are been evaluated by using the arbitrary constant that is been evaluated by using the data point from 1960. Interpret . Round your answer to two decimal places, if necessary. A)
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be decreasing at a rate of $1,162.81 billion per year.
B)
Means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be increasing at a rate of $19,312.13 billion per year.
C)
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per year.
D)
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per month.
E)
Means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be decreasing at a rate of $19,312.135 billion per month.
Question
A certain firm's marginal cost for a product is 
, its marginal revenue is 
, and its total cost of production of 11 units is $1,243. Find the profit function P.
A)
B)
C)
D)
E)
, its marginal revenue is , and its total cost of production of 11 units is $1,243. Find the profit function P.A)
B)
C)
D)
E)
Question
Suppose the rate of change of the percent P of U.S. households with cable TV can be modeled by 
, where t is the number of years past 1975. If in 1995 65.7% of households had cable TV, predict the percent of households that will have cable TV in 2025. Round your answer to one decimal place.
A)94.3%
B)90.3%
C)81.8%
D)84.3%
E)96.8%
, where t is the number of years past 1975. If in 1995 65.7% of households had cable TV, predict the percent of households that will have cable TV in 2025. Round your answer to one decimal place. A)94.3%
B)90.3%
C)81.8%
D)84.3%
E)96.8%
Question
Suppose that the marginal revenue (in dollars) from the sale of x units of a product is 
. What is the revenue from the sale of 170 units of the product? Round your answer to the nearest cent.
A)$10,487.44
B)$10,137.44
C)$15,295.41
D)$10,661.00
E)$14,771.41
. What is the revenue from the sale of 170 units of the product? Round your answer to the nearest cent. A)$10,487.44
B)$10,137.44
C)$15,295.41
D)$10,661.00
E)$14,771.41
Question
A family of functions is given below. Find the function f (x) such that the family is given by 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
If $P is invested for n years at 12% compounded continuously, the rate at which the future value is growing is 
. In how many years will the future value double? Round your answer to one decimal place.
A)9.2 years
B)7.8 years
C)5.8 years
D)11.2 years
E)10.8 years
. In how many years will the future value double? Round your answer to one decimal place. A)9.2 years
B)7.8 years
C)5.8 years
D)11.2 years
E)10.8 years
Question
A certain firm's marginal cost, in dollars, for a product is 
, its marginal revenue, in dollars, is 
, and its total cost of production of 8 items is $900. Find the profit or loss at the optimal level of production. Round your answer to the nearest dollar.
A)$172 loss
B)$172 profit
C)$820 profit
D)$820 loss
E)$400 loss
, its marginal revenue, in dollars, is , and its total cost of production of 8 items is $900. Find the profit or loss at the optimal level of production. Round your answer to the nearest dollar. A)$172 loss
B)$172 profit
C)$820 profit
D)$820 loss
E)$400 loss
Question
Suppose that the rate at which blood pressure decreases in the aorta of a normal adult after a heartbeat is 
,where t is the time in seconds. Use the function that describes the blood pressure in the aorta if 
when 
to find the blood pressure 0.9 second after a heartbeat. Round your answer to two decimal places.
A)44.24
B)169.06
C)36.68
D)37.98
E)42.74
,where t is the time in seconds. Use the function that describes the blood pressure in the aorta if when to find the blood pressure 0.9 second after a heartbeat. Round your answer to two decimal places. A)44.24
B)169.06
C)36.68
D)37.98
E)42.74
Question
Suppose that the marginal revenue for a product is 
and the marginal cost is 
, with a fixed cost of 
. Find the profit or loss from the production and sale of 3 units.
A)loss of $697
B)loss of $1,341
C)profit of $1,341
D)profit of $1,237
E)loss of $1,237
and the marginal cost is , with a fixed cost of . Find the profit or loss from the production and sale of 3 units. A)loss of $697
B)loss of $1,341
C)profit of $1,341
D)profit of $1,237
E)loss of $1,237
Question
A family of functions is given below. Find the function f (x) such that the family is given by 
. Round your answer to one decimal place, if necessary. 
A)
B)
C)
D)
E)
. Round your answer to one decimal place, if necessary. A)
B)
C)
D)
E)
Question
Suppose that the marginal revenue for a product is 
and the marginal cost is 
with a fixed cost of $900. How many units will result in a maximum profit?
A)9 units
B)8 units
C)7 units
D)11 units
E)10 units
and the marginal cost is with a fixed cost of $900. How many units will result in a maximum profit? A)9 units
B)8 units
C)7 units
D)11 units
E)10 units
Question
If the marginal cost, in dollars, for producing a product is 
, with a fixed cost of $800, what will be the cost of producing 30 units?
A)
B)
C)
D)
E)
, with a fixed cost of $800, what will be the cost of producing 30 units? A)
B)
C)
D)
E)
Question
The rate of vocabulary memorization of the average student in a certain foreign language course is given by 
, where t is the number of continuous hours of study, 
, and v is the number of words. About how many words would the average student memorize in 2 hours? Round your answer to the nearest whole number of words.
A)36 words
B)38 words
C)40 words
D)41 words
E)43 words
, where t is the number of continuous hours of study, , and v is the number of words. About how many words would the average student memorize in 2 hours? Round your answer to the nearest whole number of words. A)36 words
B)38 words
C)40 words
D)41 words
E)43 words
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Deck 13: Indefinite Integrals
1
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
2
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
3
If the marginal revenue (in dollars per unit) for a month is given by , find the total revenue from the sale of 125 units to the nearest cent.
A)$5,194.29
B)$5,193.11
C)$5,195.31
D)$41.13
E)$39.93
, find the total revenue from the sale of 125 units to the nearest cent. A)$5,194.29
B)$5,193.11
C)$5,195.31
D)$41.13
E)$39.93
$5,195.31
4
Find a function g(x) such that .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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5
Suppose that a particle has been shot into the air in such a way that the rate at which its height H (in feet per second) is changing is . If the particle is 4,200 feet high when seconds, write the formula for the height of the particle at any time t.
A)
B)
C)
D)
E)
. If the particle is 4,200 feet high when seconds, write the formula for the height of the particle at any time t.A)
B)
C)
D)
E)
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6
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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7
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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8
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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9
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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10
The DeWitt Company has found that the rate of change of its average cost of producing a product is , where x is the number of units and cost is in dollars. The average cost of producing 20 units is $40.00. Find the average cost of producing 140 units of the product. Round to the nearest dollar.
A)$46
B)$48
C)$51
D)$53
E)$58
, where x is the number of units and cost is in dollars. The average cost of producing 20 units is $40.00. Find the average cost of producing 140 units of the product. Round to the nearest dollar. A)$46
B)$48
C)$51
D)$53
E)$58
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11
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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12
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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13
Use algebra to rewrite the integrand; then integrate and simplify.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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14
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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15
Suppose that when a sense organ receives a stimulus at time t, the total number of action potentials is P(t). If the rate at which action potentials are produced is , and if there are 0 action potentials when , find the formula for P(t).
A)
B)
C)
D)
E)
, and if there are 0 action potentials when , find the formula for P(t). A)
B)
C)
D)
E)
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16
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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17
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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18
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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19
A family of functions is given and the graph of some members of the family are shown. Write the indefinite integral that gives the family.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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20
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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21
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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22
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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23
Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2).
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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24
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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25
Find du if .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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26
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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27
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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28
Suppose an oil tanker hits a reef and begins to leak. The efforts of the workers repairing the leak cause the rate at which the oil is leaking to decrease. The oil was leaking at a rate of 41 barrels per hour at the end of the first hour after the accident, and the rate is decreasing at a rate of one barrel per hour. What formula describes the rate of loss in terms of the time t that has lapsed since the leak began?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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29
The total physical output of a number of machines or workers is called physical productivity and is a function of the number of machines or workers. If is the productivity, is the marginal physical productivity. If the marginal physical productivity for bricklayers is , where P is the number of bricks laid per day and x is the number of bricklayers, find the physical productivity of 5 bricklayers. (Note: when .)
A)88,330 bricks laid per day
B)719,114 bricks laid per day
C)715,550 bricks laid per day
D)68,255 bricks laid per day
E)552,925 bricks laid per day
is the productivity, is the marginal physical productivity. If the marginal physical productivity for bricklayers is , where P is the number of bricks laid per day and x is the number of bricklayers, find the physical productivity of 5 bricklayers. (Note: when .) A)88,330 bricks laid per day
B)719,114 bricks laid per day
C)715,550 bricks laid per day
D)68,255 bricks laid per day
E)552,925 bricks laid per day
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30
The marginal revenue for a new calculator is given by , where x represents hundreds of calculators and revenue is in dollars. Find the total revenue function for these calculators.
A)
B)
C)
D)
E)
, where x represents hundreds of calculators and revenue is in dollars. Find the total revenue function for these calculators. A)
B)
C)
D)
E)
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31
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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32
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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33
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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34
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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35
Which of the following integrals cannot be integrated by using the methods studied so far?
(a)
(b)
(c)
(d)
(e)
A)a, b
B)a, b, e
C)b, c, e
D)c, d
E)d, e
(a)
(b)
(c)
(d)
(e)
A)a, b
B)a, b, e
C)b, c, e
D)c, d
E)d, e
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36
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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37
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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38
Suppose an oil tanker hits a reef and begins to leak. The efforts of the workers repairing the leak cause the rate at which the oil is leaking to decrease. The oil was leaking at a rate of 39 barrels per hour at the end of the first hour after the accident, and the rate is decreasing at a rate of one barrel per hour. How many barrels of oil will leak in the first 6 hours?
A)216 barrels
B)132 barrels
C)222 barrels
D)231 barrels
E)225 barrels
A)216 barrels
B)132 barrels
C)222 barrels
D)231 barrels
E)225 barrels
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39
Write the indefinite integral that gives the family associated with .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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40
If , find .
A)
B)
C)
D)
E)
, find . A)
B)
C)
D)
E)
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41
Because of job outsourcing, a western Pennsylvania town predicts that its public school population will decrease at the rate , where x is the number of years and N is the total school population. If N = 7,800 when x = 0, what population size is expected in 6 years? Round your answer to nearest integer when applicable.
A)6,376 students
B)7,538 students
C)8,438 students
D)7,276 students
E)9,600 students
, where x is the number of years and N is the total school population. If N = 7,800 when x = 0, what population size is expected in 6 years? Round your answer to nearest integer when applicable. A)6,376 students
B)7,538 students
C)8,438 students
D)7,276 students
E)9,600 students
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42
The rate of production of a new line of products is given by , where x is the number of items and t is the number of weeks the product has been in production. Assuming that when , find out the number of items produced in the fifth week. Round your answer to the nearest whole number.
A)98 items are produced during the fifth week
B)253 items are produced during the fifth week
C)2,083 items are produced during the fifth week
D)55,491 items are produced during the fifth week
E)258 items are produced during the fifth week
, where x is the number of items and t is the number of weeks the product has been in production. Assuming that when , find out the number of items produced in the fifth week. Round your answer to the nearest whole number. A)98 items are produced during the fifth week
B)253 items are produced during the fifth week
C)2,083 items are produced during the fifth week
D)55,491 items are produced during the fifth week
E)258 items are produced during the fifth week
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43
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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44
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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45
Evaluate the integral . If it's necessary, round your calculations to one decimal place.
A)
B)
C)
D)
E)
. If it's necessary, round your calculations to one decimal place. A)
B)
C)
D)
E)
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46
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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47
A new fast-food firm predicts that the number of franchises for its products will grow at the rate , where t is the number of years. If there is one franchise at present , how many franchises are predicted for 26 years from now?
A)2,146
B)2,176
C)2,161
D)2,314
E)2,110
, where t is the number of years. If there is one franchise at present , how many franchises are predicted for 26 years from now? A)2,146
B)2,176
C)2,161
D)2,314
E)2,110
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48
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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49
The rate of production of a new line of products is given by , where x is the number of items produced and t is the number of weeks the product has been in production. Assuming that when , find the total number of items produced as a function of time t.
A)
B)
C)
D)
E)
, where x is the number of items produced and t is the number of weeks the product has been in production. Assuming that when , find the total number of items produced as a function of time t. A)
B)
C)
D)
E)
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50
Suppose the rate of change of the interest paid on the public debt of the United States as a percent of federal expenditures can be modeled by , where t is the number of years past 1930. Use integration and the fact that in 1975, the interest paid as a percent of Federal Expenditures was 12.7, to find the function D(t) that models the interest paid on the public debt of the United States as a percent of federal expenditures. If it's necessary, round your calculations to three decimal places.
A)
B)
C)
D)
E)
, where t is the number of years past 1930. Use integration and the fact that in 1975, the interest paid as a percent of Federal Expenditures was 12.7, to find the function D(t) that models the interest paid on the public debt of the United States as a percent of federal expenditures. If it's necessary, round your calculations to three decimal places. A)
B)
C)
D)
E)
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51
Because a new employee must learn an assigned task, the employee's production will increase with time. Suppose that for the average new employee, the rate of performance is given by , where N is the number of units completed t hours after beginning a new task. If 3 units are completed after 8 hours, how many units are completed after 80 hours?
A)8
B)9
C)10
D)12
E)13
, where N is the number of units completed t hours after beginning a new task. If 3 units are completed after 8 hours, how many units are completed after 80 hours? A)8
B)9
C)10
D)12
E)13
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52
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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53
An inferior product with a large advertising budget does well when it is introduced, but sales decline as people discontinue use of the product. Suppose that the rate of weekly sales revenue is given by , where S is the sales in thousands of dollars and t is the time in weeks. Find the function that describes the weekly sales revenue if thousand dollars when .
A)
B)
C)
D)
E)
, where S is the sales in thousands of dollars and t is the time in weeks. Find the function that describes the weekly sales revenue if thousand dollars when . A)
B)
C)
D)
E)
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54
Given the functions below, decide which function is f (x), and which is a member of the family .
A)
And
Is a member of the family of
B)
And
Is a member of the family of
C)
And
Is a member of the family of
D)
And
Is a member of the family of
E)
And
Is a member of the family of
. A)
And
Is a member of the family of
B)
And
Is a member of the family of
C)
And
Is a member of the family of
D)
And
Is a member of the family of
E)
And
Is a member of the family of
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55
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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56
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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57
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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58
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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59
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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60
Evaluate the integral .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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61
If the marginal cost for a product is , and the production of 11 units results in a total cost of $687, find the total cost function C.
A)
B)
C)
D)
E)
, and the production of 11 units results in a total cost of $687, find the total cost function C.A)
B)
C)
D)
E)
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62
Suppose the rate of change of the expected life span l at birth of people born in the United States can be modeled by where t is the number of years past 1920. Use integration and the data point for 2007, to find the function that models the life span. If it's necessary, round your calculations to three decimal places,
A)
B)
C)
D)
E)
where t is the number of years past 1920. Use integration and the data point for 2007, to find the function that models the life span. If it's necessary, round your calculations to three decimal places, A)
B)
C)
D)
E)
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63
A certain firm's marginal cost for a product is , its marginal revenue is , and its total cost of production of 10 units is $530. Find the optimal level of production.
A)17 units
B)13 units
C)14 units
D)16 units
E)15 units
, its marginal revenue is , and its total cost of production of 10 units is $530. Find the optimal level of production. A)17 units
B)13 units
C)14 units
D)16 units
E)15 units
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64
If $P is invested for n years at 51% compounded continuously, the rate at which the future value is growing is . What function describes the future value at the end of n years? Round your answer to two decimal places, if necessary.
A)
B)
C)
D)
E)
. What function describes the future value at the end of n years? Round your answer to two decimal places, if necessary. A)
B)
C)
D)
E)
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65
A store finds that its sales decline after the end of an advertising campaign, with its daily sales for the period declining at the rate , where t is the number of days since the end of the campaign. Suppose that units when . About how many sales should the store expect 17 days after the end of the advertising campaign? Round your answer to the nearest whole number.
A)6,667 sales
B)6,672 sales
C)6,677 sales
D)6,670 sales
E)6,679 sales
, where t is the number of days since the end of the campaign. Suppose that units when . About how many sales should the store expect 17 days after the end of the advertising campaign? Round your answer to the nearest whole number. A)6,667 sales
B)6,672 sales
C)6,677 sales
D)6,670 sales
E)6,679 sales
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66
Suppose the rate of change of total personal income I in the United States (in billions of dollars) can be modeled by , where t is the number of years past 1960. Find the total personal income in 2016 by using the arbitrary constant that is evaluated by using the data point from 1960. Also find the rate of change of total personal income in 2016. Round your answers to two decimal places.
A)
B)
C)
D)
E)
, where t is the number of years past 1960. Find the total personal income in 2016 by using the arbitrary constant that is evaluated by using the data point from 1960. Also find the rate of change of total personal income in 2016. Round your answers to two decimal places. A)
B)
C)
D)
E)
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67
A function f (x) is given below. Find the graph of the member of the family that satisfies .
A)
B)
C)
D)
E)
that satisfies . A)
B)
C)
D)
E)
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68
Suppose the rate of change of total personal income I in the United States (in billions of dollars) can be modeled by , where t is the number of years past 1960. The value of are approximately $19,312.13 and $1,162.81 respectively which are been evaluated by using the arbitrary constant that is been evaluated by using the data point from 1960. Interpret . Round your answer to two decimal places, if necessary.
A)
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be decreasing at a rate of $1,162.81 billion per year.
B)
Means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be increasing at a rate of $19,312.13 billion per year.
C)
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per year.
D)
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per month.
E)
Means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be decreasing at a rate of $19,312.135 billion per month.
, where t is the number of years past 1960. The value of are approximately $19,312.13 and $1,162.81 respectively which are been evaluated by using the arbitrary constant that is been evaluated by using the data point from 1960. Interpret . Round your answer to two decimal places, if necessary. A)
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be decreasing at a rate of $1,162.81 billion per year.
B)
Means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be increasing at a rate of $19,312.13 billion per year.
C)
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per year.
D)
Means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per month.
E)
Means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be decreasing at a rate of $19,312.135 billion per month.
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69
A certain firm's marginal cost for a product is , its marginal revenue is , and its total cost of production of 11 units is $1,243. Find the profit function P.
A)
B)
C)
D)
E)
, its marginal revenue is , and its total cost of production of 11 units is $1,243. Find the profit function P.A)
B)
C)
D)
E)
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70
Suppose the rate of change of the percent P of U.S. households with cable TV can be modeled by , where t is the number of years past 1975. If in 1995 65.7% of households had cable TV, predict the percent of households that will have cable TV in 2025. Round your answer to one decimal place.
A)94.3%
B)90.3%
C)81.8%
D)84.3%
E)96.8%
, where t is the number of years past 1975. If in 1995 65.7% of households had cable TV, predict the percent of households that will have cable TV in 2025. Round your answer to one decimal place. A)94.3%
B)90.3%
C)81.8%
D)84.3%
E)96.8%
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71
Suppose that the marginal revenue (in dollars) from the sale of x units of a product is . What is the revenue from the sale of 170 units of the product? Round your answer to the nearest cent.
A)$10,487.44
B)$10,137.44
C)$15,295.41
D)$10,661.00
E)$14,771.41
. What is the revenue from the sale of 170 units of the product? Round your answer to the nearest cent. A)$10,487.44
B)$10,137.44
C)$15,295.41
D)$10,661.00
E)$14,771.41
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72
A family of functions is given below. Find the function f (x) such that the family is given by .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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73
If $P is invested for n years at 12% compounded continuously, the rate at which the future value is growing is . In how many years will the future value double? Round your answer to one decimal place.
A)9.2 years
B)7.8 years
C)5.8 years
D)11.2 years
E)10.8 years
. In how many years will the future value double? Round your answer to one decimal place. A)9.2 years
B)7.8 years
C)5.8 years
D)11.2 years
E)10.8 years
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74
A certain firm's marginal cost, in dollars, for a product is , its marginal revenue, in dollars, is , and its total cost of production of 8 items is $900. Find the profit or loss at the optimal level of production. Round your answer to the nearest dollar.
A)$172 loss
B)$172 profit
C)$820 profit
D)$820 loss
E)$400 loss
, its marginal revenue, in dollars, is , and its total cost of production of 8 items is $900. Find the profit or loss at the optimal level of production. Round your answer to the nearest dollar. A)$172 loss
B)$172 profit
C)$820 profit
D)$820 loss
E)$400 loss
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75
Suppose that the rate at which blood pressure decreases in the aorta of a normal adult after a heartbeat is ,where t is the time in seconds. Use the function that describes the blood pressure in the aorta if when to find the blood pressure 0.9 second after a heartbeat. Round your answer to two decimal places.
A)44.24
B)169.06
C)36.68
D)37.98
E)42.74
,where t is the time in seconds. Use the function that describes the blood pressure in the aorta if when to find the blood pressure 0.9 second after a heartbeat. Round your answer to two decimal places. A)44.24
B)169.06
C)36.68
D)37.98
E)42.74
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76
Suppose that the marginal revenue for a product is and the marginal cost is , with a fixed cost of . Find the profit or loss from the production and sale of 3 units.
A)loss of $697
B)loss of $1,341
C)profit of $1,341
D)profit of $1,237
E)loss of $1,237
and the marginal cost is , with a fixed cost of . Find the profit or loss from the production and sale of 3 units. A)loss of $697
B)loss of $1,341
C)profit of $1,341
D)profit of $1,237
E)loss of $1,237
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77
A family of functions is given below. Find the function f (x) such that the family is given by . Round your answer to one decimal place, if necessary.
A)
B)
C)
D)
E)
. Round your answer to one decimal place, if necessary. A)
B)
C)
D)
E)
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78
Suppose that the marginal revenue for a product is and the marginal cost is with a fixed cost of $900. How many units will result in a maximum profit?
A)9 units
B)8 units
C)7 units
D)11 units
E)10 units
and the marginal cost is with a fixed cost of $900. How many units will result in a maximum profit? A)9 units
B)8 units
C)7 units
D)11 units
E)10 units
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79
If the marginal cost, in dollars, for producing a product is , with a fixed cost of $800, what will be the cost of producing 30 units?
A)
B)
C)
D)
E)
, with a fixed cost of $800, what will be the cost of producing 30 units? A)
B)
C)
D)
E)
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80
The rate of vocabulary memorization of the average student in a certain foreign language course is given by , where t is the number of continuous hours of study, , and v is the number of words. About how many words would the average student memorize in 2 hours? Round your answer to the nearest whole number of words.
A)36 words
B)38 words
C)40 words
D)41 words
E)43 words
, where t is the number of continuous hours of study, , and v is the number of words. About how many words would the average student memorize in 2 hours? Round your answer to the nearest whole number of words. A)36 words
B)38 words
C)40 words
D)41 words
E)43 words
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