Question 1

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.

Accepted Answer

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

Question 2

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. ​

Accepted Answer

A) $172 loss 
B) $172 profit 
C) $820 profit 
D) $820 loss 
E) $400 loss 
A) $172 loss 
B) $172 profit 
C) $820 profit 
D) $820 loss 
E) $400 loss B

Question 3

Find the particular solution to the given differential equation. ​   when   ​

Accepted Answer

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

Question 4

Evaluate the integral   . ​

Accepted Answer

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

Question 5

Suppose that the marginal propensity to consume is   (in billions of dollars) and that consumption is $5.35 billion when disposable income is 0. Find the national consumption function C. If it's necessary, round your calculations to two decimal places.

Accepted Answer

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

Question 6

Evaluate the integral   . ​

Accepted Answer

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

Question 7

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 8

Evaluate the integral   . ​

Accepted Answer

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

Question 9

Suppose that a liquid carries a drug with concentration 0.03 g/cc into a 200-cc organ at a rate of 5 cc/s and leaves at the same rate. If initially there is 3 g of drug in the organ, find the amount A of drug in the organ as a function of time t. ​If it's necessary, round your calculations to four decimal places.

Accepted Answer

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

Question 10

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). ​

Accepted Answer

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

Question 11

Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2). ​   ​

Accepted Answer

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

Question 12

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. ​   ​

Accepted Answer

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

Question 13

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. ​

Accepted Answer

A) $5,194.29 
B) $5,193.11 
C) $5,195.31 
D) $41.13 
E) $39.93 
A) $5,194.29 
B) $5,193.11 
C) $5,195.31 
D) $41.13 
E) $39.93

Question 14

Evaluate the integral   . ​

Accepted Answer

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

Question 15

Evaluate the integral   . ​

Accepted Answer

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

Question 16

Suppose that the marginal propensity to save is   (in billions of dollars) and that consumption is $9 billion when disposable income is 0. Find the national consumption function C. Round numbers in our answer to two decimal places when appropriate. If it's necessary, round your calculations to two decimal places. ​

Accepted Answer

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

Question 17

Find the general solution to the differential equation   . ​

Accepted Answer

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

Question 18

The average cost of a product, in dollars, changes at the rate   and the average cost of 12 units is $25.00. Find the average cost of 24 units. Round your answer to the nearest cent. ​

Accepted Answer

A) $600.00 
B) $25.50 
C) $50.00 
D) $30.60 
E) $1.50 
A) $600.00 
B) $25.50 
C) $50.00 
D) $30.60 
E) $1.50

Question 19

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. ​

Accepted Answer

A) 9.2 years 
B) 7.8 years 
C) 5.8 years 
D) 11.2 years 
E) 10.8 years 
A) 9.2 years 
B) 7.8 years 
C) 5.8 years 
D) 11.2 years 
E) 10.8 years

Question 20

Suppose that the marginal propensity to save is   (in billions of dollars), and that consumption is $8.30 billion when disposable income is 0. Find the national consumption function. Round your answer to two decimal places. ​

Accepted Answer

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

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 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.

Find the particular solution to the given differential equation. when

Evaluate the integral .

Suppose that the marginal propensity to consume is (in billions of dollars) and that consumption is $5.35 billion when disposable income is 0. Find the national consumption function C. If it's necessary, round your calculations to two decimal places.

Evaluate the integral .

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

Evaluate the integral .

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).

Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2).

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.

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.

Evaluate the integral .

Evaluate the integral .

Find the general solution to the differential equation .

The average cost of a product, in dollars, changes at the rate and the average cost of 12 units is $25.00. Find the average cost of 24 units. Round your answer to the nearest cent.

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.

Suppose that the marginal propensity to save is (in billions of dollars), and that consumption is $8.30 billion when disposable income is 0. Find the national consumption function. Round your answer to two decimal places.

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

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Exam 13: Indefinite Integrals

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 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. ​

Find the particular solution to the given differential equation. ​ when ​

Evaluate the integral . ​

Suppose that the marginal propensity to consume is (in billions of dollars) and that consumption is $5.35 billion when disposable income is 0. Find the national consumption function C. If it's necessary, round your calculations to two decimal places.

Evaluate the integral . ​

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

Evaluate the integral . ​

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). ​

Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2). ​ ​

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. ​ ​

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. ​

Evaluate the integral . ​

Evaluate the integral . ​

Find the general solution to the differential equation . ​

The average cost of a product, in dollars, changes at the rate and the average cost of 12 units is $25.00. Find the average cost of 24 units. Round your answer to the nearest cent. ​

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. ​

Suppose that the marginal propensity to save is (in billions of dollars), and that consumption is $8.30 billion when disposable income is 0. Find the national consumption function. Round your answer to two decimal places. ​

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, 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.

Find the particular solution to the given differential equation. when

Evaluate the integral .

Evaluate the integral .

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

Evaluate the integral .

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).

Evaluate the integral below and sketch the graph of the family member that passes through the point (1, 2).

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.

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.

Evaluate the integral .

Evaluate the integral .

Find the general solution to the differential equation .

The average cost of a product, in dollars, changes at the rate and the average cost of 12 units is $25.00. Find the average cost of 24 units. Round your answer to the nearest cent.

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.

Suppose that the marginal propensity to save is (in billions of dollars), and that consumption is $8.30 billion when disposable income is 0. Find the national consumption function. Round your answer to two decimal places.