MTH 135 Homework Assignment for Week 7

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the integral.

1) 1) _______

A) B)

C) D)

2) 2) _______

A) B)

C) D)

Provide an appropriate response.

3) Find f(x) if and 3) _______

A) B) C) D)

Solve the problem.

4) The marginal revenue from the sale of compact discs is given by and where R(x) is the

revenue in dollars. Find the price-demand equation. 4) _______

A) B) C) D)

Find the integral.

5) 5) _______

A) – 2 ln + C B)

C) D) 2 ln + C

6) 6) _______

A) B)

C) D)

Solve the problem.

7) A company has found that the marginal cost of a new production line (in thousands) is where x is the

number of years the line is in use. Find the total cost function for the production line (in thousands). The fixed cost is

$20,000. 7) _______

A) C(x) = + 20 B) C(x) = 9 ln (x + e) + 11

C) C(x) = + 11 D) C(x) = 9 ln (x + e) + 20

Provide an appropriate response.

8) Find the general solution for the differential equation 8) _______

A) B) C) D)

9) Find the particular solution for the differential equation y’ = 4x ; y(0) = 20. 9) _______

A) y = 4x – + 22 B) y = 2x – + 21

C) y = 2x + 20 D) y = 4x – + 21

Match the differential equation with the appropriate slope field.

10) = – 10) ______

A)

B)

C)

D)

Solve the problem.

11) A single injection of a drug is administered to a patient. The amount Q in the body then decreases at a rate

proportional to the amount present, and for this particular drug the rate is 3% per hour. Thus, with

where t is time in hours. If the initial injection is 4 milliliters about how many hours after the drug

is given will there be 2 milliliters of the drug remaining in the body? (Round answer to the nearest tenth of an hour.)

11) ______

A) 21.3 hours B) 69.3 hours C) 23.1 hours D) 11.3 hours

Identify the rectangles shown in the graph as left rectangles, right rectangles, or neither.

12)

12) ______

A) left rectangles B) neither C) right rectangles

Provide an appropriate response.

13) Divide the interval [0, 8] into four equal subintervals and draw in the corresponding left rectangles.

13) ______

A)

B)

C)

D)

Approximate the area under the graph of f(x) and above the x-axis using n rectangles.

14) f(x) = + 2; interval [0, 5]; n = 5; compute 14) ______

A) 66 B) 32 C) 40 D) 65

Evaluate the integral.

15) 15) ______

A) 2 B) -7 C) 12 D) 7

16) . 16) ______

A) 288 B) 24 C) 192 D) 128

17) dx 17) ______

A) -5 B) – C) 0 D) 5

Provide an appropriate response.

18) Find the average value of the function y = 5 – over the interval [- 3, 2]. 18) ______

A) B) C) – D)

Solve the problem.

19) A drug is injected into the bloodstream of a patient through her right arm. The concentration of the drug, C(t) (in

milligrams per cubic centimeter), in the blood stream of the left arm t hours after the injection is given by

What is the average concentration of the drug in the bloodstream of the left arm during the first two hours after the

injection? 19) ______

A) 0.344 milligrams per cubic centimeter B) 0.060 milligrams per cubic centimeter

C) 0.241 milligrams per cubic centimeter D) 0.121 milligrams per cubic centimeter

MTH 135 Participation Exercise for Week 7

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the integral.

1) dt 1) _______

A) 5 – 5 – 2t + C B) – – 2t + C

C) – 5 – 2t + C D) 10t – 5 + C

2) 2) _______

A) B)

C) D)

Provide an appropriate response.

3) Find f(x) if . 3) _______

A) B)

C) D)

Solve the problem.

4) A company finds that consumer demand quantity changes with respect to price at a rate given by

Find the demand function if the company knows that 842 units of the product are demanded when the price is $5 per

unit. 4) _______

A) D(p) = + 842 B) D(p) = + 442

C) D(p) = + 842 D) D(p) = + 442

5) A newspaper is launching a new advertising campaign in order to increase the number of daily subscribers. The

newspaper currently (t = 0) has 26,000 daily subscribers and management expects that number, S(t), to grow at the rate

of subscribers per day, where t is the number of days since the campaign began. How long (to the nearest

day) should the campaign last if the newspaper wants the number of daily subscribers to grow to 49,000? 5) _______

A) 33 days B) 44 days C) 57 days D) 69 days

Find the integral.

6) 6) _______

A) + C B) (7x + 4) + C

C) 7 + C D)

7) 7) _______

A) + C B) + C C) + C D) + C

8) dx 8) _______

A) + C B) + C

C) 2 + C D) – + C

9) 9) _______

A) B)

C) D)

Solve the problem.

10) The marginal price for a weekly demand of x bottles of cough medicine in a drug store is given by

Find the price-demand equation if the weekly demand is 125 when the price of a bottle of cough medicine is $4. What is

the weekly demand (to the nearest bottle) when the price is $3? 10) ______

A) B)

C) D)

11) A manufacturing company is ready to introduce a new product with a national sales campaign. After extensive test

marketing, the market research department estimates that sales (in millions of dollars) will increase at the monthly rate of

t months after the national campaign has started. What will the total sales be five months

after the beginning of the campaign if we assume zero sales at the beginning of the campaign? (Round the answer to the

nearest million.) 11) ______

A) B) C) D)

Provide an appropriate response.

12) Find the general solution for the differential equation y’= 30×2 12) ______

A) 10×3 + C B) + C C) 30×3 + C D) x3 + C

13) Find the particular solution for the differential equation 13) ______

A) y = ln + ln 2 + 3 B) y = ln – ln 2 + 3

C) y = ln D)

Match the differential equation with the appropriate slope field.

14) = 14) ______

A)

B)

C)

D)

Provide an appropriate response.

15) Graph the following example of exponential decay: , 0 ≤ t ≤ 45, 0 ≤ y ≤ 900.

15) ______

A)

B)

C)

D)

Solve the problem.

16) Find the amount A in an account (to the nearest dollar) after 5 years if and 16)

______

A) $1000 B) $919 C) $1200 D) $1100

Provide an appropriate response.

17) Graph the following example of exponential decay: , 0 ≤ t ≤ 45, 0 ≤ y ≤ 900.

17) ______

A)

B)

C)

D)

Identify the rectangles shown in the graph as left rectangles, right rectangles, or neither.

18)

18) ______

A) right rectangles B) neither C) left rectangles

Approximate the area under the graph of f(x) and above the x-axis using n rectangles.

19) f(x) = 2x + 3 from x = 0 to x = 2; n = 4; compute 19) ______

A) 17 B) 15 C) 13 D) 11

Provide an appropriate response.

20) Calculate the Riemann sum, , for the function on the interval Partition into

five subintervals of equal length and for each subinterval let be the midpoint. 20) ______

A) -38 B) 40 C) 38 D) – 40

21) Given and use properties of definite integrals to evaluate

21) ______

A) 24 B) 18 C) 54 D) 13

22) Given and find 22) ______

A) 28 B) 2 C) 26 D) 30

Solve the problem.

23) Test marketing for a new health-food snack product in a selected area suggests that sales (in thousands of dollars)

will increase at a rate given by t months after an aggressive national advertising campaign is begun.

Find total sales during the second 12 months of the campaign. (Round to the nearest thousand dollars.) 23) ______

A) $693,000 B) $267,000 C) $449,000 D) $511,000

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

24) (A) Calculate the change in F(x) from to .

(B) Graph (x) and use geometric formulas to calculate the area between the graph of (x) and the x-axis from to

.

(C) What guarantees that your answers to (A) and (B) are equal?

F(x) = x( x + 4)

24) _____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Evaluate the integral.

25) dx 25) ______

A) B) 625 C) D)

26) dx 26) ______

A) – B) 7 – 1 C) 7 – 7 D) 7

Provide an appropriate response.

27) Find the average value of the function y = 2 over the interval [- 2, 2]. 27) ______

A) B) C) 0 D)

Solve the problem.

28) A population of bacteria grows at a rate of P'(t) = 12 where t is time in hours. Determine how much the population

increases from to Round your answer to two decimal places. 28) ______

A) 229.03 B) 241.03 C) 470.06 D) 235.03