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mth135participationexerciseforweek7.pdf
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'= 30x2 12) ______
A) 10x3 + C B) + C C) 30x3 + 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
