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MTH 135 Homework Assignment for Week 6

Name___________________________________

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

Find the integral.

1) 1) _______

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

2) 2) _______

A) + C B) 3x + C C) 0 D) 3 + C

Provide an appropriate response.

3) Find f(x) if and 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) = + 442 B) D(p) = + 842

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

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

Find the integral.

6)

6) _______

A) B) 2 ln + C

C) – 2 ln + C D)

7) dx 7) _______

A) + C B) – + C

C) 2 + C D) + C

Solve the problem.

8) 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? 8) _______

A) B)

C) D)

Provide an appropriate response.

9) Find the general solution for the differential equation y’ = 5e3x 9) _______

A) e3x + C B) 15e3x + C C) 5e3x + C D) e3x + C

10) Find the particular solution for the differential equation 10) ______

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

C) y = ln – ln 2 + 3 D) y = ln

Match the differential equation with the appropriate slope field.

11) = y + 2 11) ______

A)

B)

C)

D)

Provide an appropriate response.

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

12) ______

A)

B)

C)

D)

Solve the problem.

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

13) ______

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

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

14)

14) ______

A) left rectangles B) right rectangles C) neither

Provide an appropriate response.

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

15) ______

A)

B)

C)

D)

16) Given and use properties of definite integrals to evaluate

16) ______

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

17) Given and find 17) ______

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

Solve the problem.

18) 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.) 18) ______

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

Evaluate the integral.

19) dx 19) ______

A) B) 625 C)

D)

20) dx 20) ______

A) 7 – 7 B) 7 – 1 C) 7 D) –

Provide an appropriate response.

21) Find the average value of the function y = 2 over the interval [- 2, 2]. 21) ______

A) 0 B) C) D)

Solve the problem.

22) 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. 22) ______

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

MTH 135 Participation Assignment for Week 6

Name___________________________________

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

Find the integral.

1) 1) _______

A) 9 – + 6x + C B) 9 – + 6x + C

C) – + 6x + C D) – + 6x + C

2) 2) _______

A) + C B) + C C) – + C D) -91 + C

Provide an appropriate response.

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

A) B)

C) D)

Solve the problem.

4) The rate of change in a person’s body temperature, with respect to the dosage of x milligrams of a drug, is given by

One milligram raises the temperature 3.5°C. Find the function giving the total change. 4) _______

A) D(x) = ln – 4.8 B) D(x) = ln – 3.5

C) D(x) = 4 ln + 3.5 D) D(x) = 4 ln – 4.8

Find the integral.

5) 5) _______

A) B)

C) D)

6) 6) _______

A) – + C B) – + C

C) + C D) – + C

7) 7) _______

A) + C B) + C

C) + C D) + C

Solve the problem.

8) The rate of expenditure for maintenance of a particular machine is given by M'(x) = 12x , where x is time

measured in years. Total maintenance costs through the second year are $105. Find the total maintenance function.

8) _______

A) M(x) = 4 – 3 B) M(x) = 12 – 3

C) M(x) = 4 – 93 D) M(x) = 12 – 93

Provide an appropriate response.

9) Find the general solution for the differential equation y’= 30×2 9) _______

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

10) Find the particular solution for the differential equation y’ = 4x + 7; y(0) = -12. 10) ______

A) y = 4 + 7x – 6 B) y = 2 + 7x – 6

C) y = 4 + 7x – 12 D) y = 2 + 7x – 12

Match the differential equation with the appropriate slope field.

11) = x – y 11) ______

A)

B)

C)

D)

Provide an appropriate response.

12) Graph the following example of unlimited growth: y = 450 , 0 ≤ t ≤ 12, 0 ≤ y ≤ 4500.

12) ______

A)

B)

C)

D)

Solve the problem.

13) If the marginal price at x units of demand per week is proportional to the price p, and if at $80 there is no weekly

demand and if at $50.18 there is a weekly demand of 8 units find the price-demand equation.

13) ______

A) B)

C) D)

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

14)

14) ______

A) neither B) left rectangles C) right rectangles

Provide an appropriate response.

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

15) ______

A)

B)

C)

D)

16) 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. 16) ______

A) – 40 B) -38 C) 38 D) 40

17) How large should n (n an integer) be chosen for and for the approximation of to be within

0.05 of the true value? 17) ______

A) n ≥ 42 B) n ≥ 28 C) n ≥ 90 D) n ≥ 5

18) Given that find the definite integral

18) ______

A) B) C) – 6 D)

Evaluate the integral.

19) 19) ______

A) 8.5 B) 8.67 C) 9.17 D) 12.33

20) 20) ______

A) 52.5 B) 34 C) 58 D) 76

Provide an appropriate response.

21) Find the average value of the function over the interval Round your answer to two decimal

places. 21) ______

A) 73.13 B) 45.71 C) 1462.63 D) 2.29

Solve the problem.

22) The number of cheeseburgers (in thousands) sold each day by a chain of restaurants t days after the end of an

advertising campaign is given by What is the average number of cheeseburgers sold each day during

the first 7 days after the end of the advertising campaign? 22) ______

A) 5904 cheeseburgers B) 4770 cheeseburgers

C) 3740 cheeseburgers D) 4821 cheeseburgers

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