Question 1

Evaluate the integral   . ​

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Question 2

Evaluate the integral   . ​

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Question 3

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. ​

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Question 4

Find the general solution to the differential equation   . ​

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Question 5

Evaluate the integral   . ​

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Question 6

If consumption is $8 billion when disposable income is 0, and if the marginal propensity to consume is   (in billions of dollars), find the national consumption function. If it's necessary, round your answer to two decimal places. ​

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Question 7

Suppose that a liquid carries a drug into a 400-cc organ at a rate of 20 cc/s and leaves the organ at the same rate. Suppose that the concentration of the drug entering is 0.25 g/cc. Find the amount A of drug in the organ as a function of time t if initially there is none in the organ. If it's necessary, round your calculations to four decimal places. ​

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Question 8

A certain radioactive substance has a half-life of 75 hours. Find how long it will take, to the nearest hour, for 75% of the radioactivity to be dissipated if the amount of material x satisfies   (t in hours). Round your answer to the nearest hour. ​

Accepted Answer

A) 182 hours 
B) 171 hours 
C) 157 hours 
D) 150 hours 
E) 31 hours 
A) 182 hours 
B) 171 hours 
C) 157 hours 
D) 150 hours 
E) 31 hours

Question 9

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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Question 10

Evaluate the integral   . ​

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Question 11

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 12

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. ​

Accepted Answer

A) loss of $697 
B) loss of $1,341 
C) profit of $1,341 
D) profit of $1,237 
E) loss of $1,237 
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 13

Find the particular solution. ​   ​

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Question 14

When the interest on an investment is compounded continuously, the investment grows at a rate that is proportional to the amount in the account. If $25,000 is invested (when   ) and the amount in the account after 18 years is $46,940.26, find the interest rate on this investment? Round to one decimal place. ​

Accepted Answer

A) 3.0% 
B) 3.5% 
C) 4.0% 
D) 4.5% 
E) 5.0% 
A) 3.0% 
B) 3.5% 
C) 4.0% 
D) 4.5% 
E) 5.0%

Question 15

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 $210,000. Find   . Round your answer to three decimal places, if necessary. ​

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Question 16

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. ​

Accepted Answer

A) 6,376 students 
B) 7,538 students 
C) 8,438 students 
D) 7,276 students 
E) 9,600 students 
A) 6,376 students 
B) 7,538 students 
C) 8,438 students 
D) 7,276 students 
E) 9,600 students

Question 17

If   , find   . ​

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Question 18

Find the particular solution to the differential equation   that satisfies   when   . ​

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Question 19

The impact of inflation on a fixed pension can be severe. If P represents the purchasing power (in dollars) of a $50,000 pension, then the effect of a 2.5% inflation rate can be modeled by the differential equation   , where t is in years. Find the purchasing power of the pension after 35 years. Round to the nearest dollar. ​

Accepted Answer

A) $27,096 
B) $25,012 
C) $16,674 
D) $31,265 
E) $20,843 
A) $27,096 
B) $25,012 
C) $16,674 
D) $31,265 
E) $20,843

Question 20

Use integration to find the general solution to the differential equation   . ​

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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 the general solution to the differential equation .

Evaluate the integral .

If consumption is $8 billion when disposable income is 0, and if the marginal propensity to consume is (in billions of dollars), find the national consumption function. If it's necessary, round your answer to two decimal places.

A certain radioactive substance has a half-life of 75 hours. Find how long it will take, to the nearest hour, for 75% of the radioactivity to be dissipated if the amount of material x satisfies (t in hours). Round your answer to the nearest hour.

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.

Evaluate the integral .

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.

Find the particular 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 $210,000. Find . Round your answer to three decimal places, if necessary.

If , find .

Find the particular solution to the differential equation that satisfies when .

Use integration to find the general solution to the differential equation .

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

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 the general solution to the differential equation . ​

Evaluate the integral . ​

If consumption is $8 billion when disposable income is 0, and if the marginal propensity to consume is (in billions of dollars), find the national consumption function. If it's necessary, round your answer to two decimal places. ​

A certain radioactive substance has a half-life of 75 hours. Find how long it will take, to the nearest hour, for 75% of the radioactivity to be dissipated if the amount of material x satisfies (t in hours). Round your answer to the nearest hour. ​

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.

Evaluate the integral . ​

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. ​

Find the particular 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 $210,000. Find . Round your answer to three decimal places, if necessary. ​

If , find . ​

Find the particular solution to the differential equation that satisfies when . ​

Use integration to find the general solution to the differential equation . ​

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

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 the general solution to the differential equation .

Evaluate the integral .

If consumption is $8 billion when disposable income is 0, and if the marginal propensity to consume is (in billions of dollars), find the national consumption function. If it's necessary, round your answer to two decimal places.

A certain radioactive substance has a half-life of 75 hours. Find how long it will take, to the nearest hour, for 75% of the radioactivity to be dissipated if the amount of material x satisfies (t in hours). Round your answer to the nearest hour.

Evaluate the integral .

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.

Find the particular 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 $210,000. Find . Round your answer to three decimal places, if necessary.

If , find .

Find the particular solution to the differential equation that satisfies when .

Use integration to find the general solution to the differential equation .