Question 1

A certain firm's marginal cost for a product is   , its marginal revenue is   , and its total cost of production of 15 units is $1,050. Find the optimal level of production. ​

Accepted Answer

A)  14 units 
B)  10 units 
C)  11 units 
D)  13 units 
E)  12 units 
A)  14 units 
B)  10 units 
C)  11 units 
D)  13 units 
E)  12 units

Question 2

Evaluate the integral   . ​

Accepted Answer

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

Question 3

Evaluate the integral   . ​

Accepted Answer

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

Question 4

If consumption C is $1 billion when disposable income y is 0, and if the marginal propensity to consume is 0.60, find the national consumption function C as a function of y (in billions of dollars). Round your answer to two decimal places. ​

Accepted Answer

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

Question 5

Find du if   . ​

Accepted Answer

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

Question 6

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? ​

Accepted Answer

A)  8 
B)  9 
C)  10 
D)  12 
E)  13 
A)  8 
B)  9 
C)  10 
D)  12 
E)  13

Question 7

Evaluate the integral   . ​

Accepted Answer

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B)    
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Question 8

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 50 days after the end of the advertising campaign? Round your answer to the nearest whole number. ​

Accepted Answer

A)  6,641 sales 
B)  6,646 sales 
C)  6,651 sales 
D)  6,644 sales 
E)  6,653 sales 
A)  6,641 sales 
B)  6,646 sales 
C)  6,651 sales 
D)  6,644 sales 
E)  6,653 sales

Question 9

If consumption is $5 billion when disposable income is 0, and if the marginal propensity to consume is 0.60, what is consumption when disposable income is 40 billion? If it's necessary, round your answer to one decimal place. ​

Accepted Answer

A)  $200.6 billion 
B)  $485 billion 
C)  $29 billion 
D)  $17 billion 
E)  $4,000.6 billion 
A)  $200.6 billion 
B)  $485 billion 
C)  $29 billion 
D)  $17 billion 
E)  $4,000.6 billion

Question 10

Consider the following function:   . Of which of the following differential equations is this a solution? ​

Accepted Answer

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

Question 11

Suppose that the marginal cost for a certain product is given by   , where x is in thousand of units and cost is in thousands of dollars. Suppose further that fixed costs are $200,000. Find   . Round your answer to three decimal places, if necessary. ​

Accepted Answer

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

Question 12

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. ​
 
​

Accepted Answer

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

Question 13

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. ​

Accepted Answer

A)  $46 
B)  $48 
C)  $51 
D)  $53 
E)  $58 
A)  $46 
B)  $48 
C)  $51 
D)  $53 
E)  $58

Question 14

Evaluate the integral   . ​

Accepted Answer

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B)    
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D)    
E)    
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B)    
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D)    
E)

Question 15

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 2000 67.8% of households had cable TV, predict the percent of households that will have cable TV in 2010. Round your answer to one decimal place. ​

Accepted Answer

A)  76.7% 
B)  72.7% 
C)  64.2% 
D)  66.7% 
E)  79.2% 
A)  76.7% 
B)  72.7% 
C)  64.2% 
D)  66.7% 
E)  79.2%

Question 16

Evaluate the integral   . ​

Accepted Answer

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Question 17

A function f (x) is given below. Find the graph of the member of the family   that satisfies   . ​   ​

Accepted Answer

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E)  ​​  
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C)  ​  
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D)  ​  
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E)  ​​  
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Question 18

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? ​

Accepted Answer

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D)    
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Question 19

Evaluate the integral   . ​

Accepted Answer

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Question 20

Evaluate the integral   . ​

Accepted Answer

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A certain firm's marginal cost for a product is , its marginal revenue is , and its total cost of production of 15 units is $1,050. Find the optimal level of production.

Evaluate the integral .

Evaluate the integral .

If consumption C is $1 billion when disposable income y is 0, and if the marginal propensity to consume is 0.60, find the national consumption function C as a function of y (in billions of dollars). Round your answer to two decimal places.

Find du if .

Evaluate the integral .

If consumption is $5 billion when disposable income is 0, and if the marginal propensity to consume is 0.60, what is consumption when disposable income is 40 billion? If it's necessary, round your answer to one decimal place.

Consider the following function: . Of which of the following differential equations is this a solution?

Suppose that the marginal cost for a certain product is given by , where x is in thousand of units and cost is in thousands of dollars. Suppose further that fixed costs are $200,000. Find . Round your answer to three decimal places, if necessary.

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.

Evaluate the integral .

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 2000 67.8% of households had cable TV, predict the percent of households that will have cable TV in 2010. Round your answer to one decimal place.

Evaluate the integral .

A function f (x) is given below. Find the graph of the member of the family that satisfies .

Evaluate the integral .

Evaluate the integral .

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

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Algebraic Concepts 3

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Exam 12: Indefinite Integrals

A certain firm's marginal cost for a product is , its marginal revenue is , and its total cost of production of 15 units is $1,050. Find the optimal level of production. ​

Evaluate the integral . ​

Evaluate the integral . ​

If consumption C is $1 billion when disposable income y is 0, and if the marginal propensity to consume is 0.60, find the national consumption function C as a function of y (in billions of dollars). Round your answer to two decimal places. ​

Find du if . ​

Evaluate the integral . ​

If consumption is $5 billion when disposable income is 0, and if the marginal propensity to consume is 0.60, what is consumption when disposable income is 40 billion? If it's necessary, round your answer to one decimal place. ​

Consider the following function: . Of which of the following differential equations is this a solution? ​

Suppose that the marginal cost for a certain product is given by , where x is in thousand of units and cost is in thousands of dollars. Suppose further that fixed costs are $200,000. Find . Round your answer to three decimal places, if necessary. ​

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. ​

Evaluate the integral . ​

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 2000 67.8% of households had cable TV, predict the percent of households that will have cable TV in 2010. Round your answer to one decimal place. ​

Evaluate the integral . ​

A function f (x) is given below. Find the graph of the member of the family that satisfies . ​ ​

Evaluate the integral . ​

Evaluate the integral . ​

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability and Data Description

Derivatives

Derivatives

Derivatives Continued

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

A certain firm's marginal cost for a product is , its marginal revenue is , and its total cost of production of 15 units is $1,050. Find the optimal level of production.

Evaluate the integral .

Evaluate the integral .

If consumption C is $1 billion when disposable income y is 0, and if the marginal propensity to consume is 0.60, find the national consumption function C as a function of y (in billions of dollars). Round your answer to two decimal places.

Find du if .

Evaluate the integral .

If consumption is $5 billion when disposable income is 0, and if the marginal propensity to consume is 0.60, what is consumption when disposable income is 40 billion? If it's necessary, round your answer to one decimal place.

Consider the following function: . Of which of the following differential equations is this a solution?

Suppose that the marginal cost for a certain product is given by , where x is in thousand of units and cost is in thousands of dollars. Suppose further that fixed costs are $200,000. Find . Round your answer to three decimal places, if necessary.

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.

Evaluate the integral .

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 2000 67.8% of households had cable TV, predict the percent of households that will have cable TV in 2010. Round your answer to one decimal place.

Evaluate the integral .

A function f (x) is given below. Find the graph of the member of the family that satisfies .

Evaluate the integral .

Evaluate the integral .