Question 1

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. ​

Accepted Answer

A) 17 units 
B) 13 units 
C) 14 units 
D) 16 units 
E) 15 units 
A) 17 units 
B) 13 units 
C) 14 units 
D) 16 units 
E) 15 units

Question 2

Evaluate the integral   . ​

Accepted Answer

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

Question 3

For which of the following differential equations is   a solution? ​

Accepted Answer

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

Question 4

If consumption is $1 billion when disposable income is 0, and if the marginal propensity to consume is 0.50, what is consumption when disposable income is 50 billion? If it's necessary, round your answer to one decimal place. ​

Accepted Answer

A) $50.5 billion 
B) $626 billion 
C) $26 billion 
D) $13.5 billion 
E) $1,250.5 billion 
A) $50.5 billion 
B) $626 billion 
C) $26 billion 
D) $13.5 billion 
E) $1,250.5 billion

Question 5

Find the particular solution. ​     ​

Accepted Answer

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

Question 6

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? ​

Accepted Answer

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

Question 7

Evaluate the integral   . ​

Accepted Answer

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

Question 8

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   . ​

Accepted Answer

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

Question 9

When interest is compounded continuously, the rate of change of the amount x of the investment is proportional to the amount present. In this case, the proportionality constant is the annual interest rate r (as a decimal); that is,   . If $2,500 is invested at 7%, compounded continuously, what will be the future value of this investment after 12 years? Round to the nearest cent. ​

Accepted Answer

A) $4,600.00 
B) $5,776.80 
C) $5,630.48 
D) $5,708.32 
E) $5,790.92 
A) $4,600.00 
B) $5,776.80 
C) $5,630.48 
D) $5,708.32 
E) $5,790.92

Question 10

Evaluate the integral   . ​

Accepted Answer

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

Question 11

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. ​

Accepted Answer

A) 36 words 
B) 38 words 
C) 40 words 
D) 41 words 
E) 43 words 
A) 36 words 
B) 38 words 
C) 40 words 
D) 41 words 
E) 43 words

Question 12

Let V denote the volume of a tumor, and suppose that the growth rate of the tumor satisfies   . If the initial volume of the tumor is 1.89 units, find an equation for V as a function of t. If it's necessary, round your calculations to two decimal places. ​

Accepted Answer

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

Question 13

Evaluate the integral   . ​

Accepted Answer

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

Question 14

Evaluate the integral   . ​

Accepted Answer

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

Question 15

Suppose that the marginal propensity to consume is   (in billions of dollars), and that consumption is $5.33 billion when disposable income is 0. Find the national consumption function. If it's necessary, round your calculations to four decimal places. ​

Accepted Answer

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

Question 16

Evaluate the integral   . ​

Accepted Answer

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

Question 17

Evaluate the integral   . ​

Accepted Answer

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

Question 18

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. ​

Accepted Answer

A) 6,667 sales 
B) 6,672 sales 
C) 6,677 sales 
D) 6,670 sales 
E) 6,679 sales 
A) 6,667 sales 
B) 6,672 sales 
C) 6,677 sales 
D) 6,670 sales 
E) 6,679 sales

Question 19

Evaluate the integral   . ​

Accepted Answer

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

Question 20

Evaluate the integral   . ​

Accepted Answer

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

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.

Evaluate the integral .

For which of the following differential equations is a solution?

If consumption is $1 billion when disposable income is 0, and if the marginal propensity to consume is 0.50, what is consumption when disposable income is 50 billion? If it's necessary, round your answer to one decimal place.

Find the particular solution.

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?

Evaluate the integral .

Evaluate the integral .

Let V denote the volume of a tumor, and suppose that the growth rate of the tumor satisfies . If the initial volume of the tumor is 1.89 units, find an equation for V as a function of t. If it's necessary, round your calculations to two decimal places.

Evaluate the integral .

Evaluate the integral .

Suppose that the marginal propensity to consume is (in billions of dollars), and that consumption is $5.33 billion when disposable income is 0. Find the national consumption function. If it's necessary, round your calculations to four decimal places.

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Algebraic Concepts

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; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 13: Indefinite Integrals

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. ​

Evaluate the integral . ​

For which of the following differential equations is a solution? ​

If consumption is $1 billion when disposable income is 0, and if the marginal propensity to consume is 0.50, what is consumption when disposable income is 50 billion? If it's necessary, round your answer to one decimal place. ​

Find the particular solution. ​ ​

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? ​

Evaluate the integral . ​

Evaluate the integral . ​

Let V denote the volume of a tumor, and suppose that the growth rate of the tumor satisfies . If the initial volume of the tumor is 1.89 units, find an equation for V as a function of t. If it's necessary, round your calculations to two decimal places. ​

Evaluate the integral . ​

Evaluate the integral . ​

Suppose that the marginal propensity to consume is (in billions of dollars), and that consumption is $5.33 billion when disposable income is 0. Find the national consumption function. If it's necessary, round your calculations to four decimal places. ​

Evaluate the integral . ​

Evaluate the integral . ​

Evaluate the integral . ​

Evaluate the integral . ​

Algebraic Concepts

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; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

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.

Evaluate the integral .

For which of the following differential equations is a solution?

If consumption is $1 billion when disposable income is 0, and if the marginal propensity to consume is 0.50, what is consumption when disposable income is 50 billion? If it's necessary, round your answer to one decimal place.

Find the particular solution.

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?

Evaluate the integral .

Evaluate the integral .

Let V denote the volume of a tumor, and suppose that the growth rate of the tumor satisfies . If the initial volume of the tumor is 1.89 units, find an equation for V as a function of t. If it's necessary, round your calculations to two decimal places.

Evaluate the integral .

Evaluate the integral .

Suppose that the marginal propensity to consume is (in billions of dollars), and that consumption is $5.33 billion when disposable income is 0. Find the national consumption function. If it's necessary, round your calculations to four decimal places.

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .

Evaluate the integral .