Name:    MAT 121 Chapter 5 Test

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

Evaluate the expression.

 A 3 B 2 C 27 D 24

2.

Evaluate the expression.

 A B C D E

3.

Simplify the expression.

 A B C D E

4.

Simplify the expression.

 A B C D

5.

Solve the equation for x.

 A x  =  2 B x =  16 C x  =  8 D x  =  7

6.

Solve the equation for x.

 A B C D E

7.

Solve the equation for x.

 A B C D

8.

Sketch the graphs of the given functions on the same axes.

 A C B

9.

Sketch the graphs of the given functions on the same axes.

 A C B

10.

Sketch the graphs of the functions on the same axes.

 A D B E C

11.

The concentration of a drug in an organ at any time t (in seconds) is given by

where C(t) is measured in milligrams/cubic centimeter. What is the concentration to four decimal places of the drug in the organ after 15 sec?
 A B C D

12.

Express the equation in logarithmic form.

 A B C D

13.

Express the equation in logarithmic form.

 A B C D

14.

Sketch the graph of the equation.

 A D B E C

15.

Use logarithms to solve the equation for t. Round your answer to four decimal places.

 A B C D

16.

Use logarithms to solve the equation for t.

 A B C D

17.

Use logarithms to solve the equation for t. Please round the answer to four decimal places.

 A B C D E

18.

The height (in feet) of a certain kind of tree is approximated by   where is the age of the tree in years. Estimate the age of an 70-ft tree. Round your answer to the nearest hundredth.
 A 17.53 years B 16.69 years C 16.10 years D 19.70 years

19.

The concentration of a drug in an organ at any time t (in seconds) is given by     where is measured in grams/cubic centimeter . How long would it take for the concentration of the drug in the organ to reach 0.18?

 A sec B sec C sec D sec E sec

20.

Use the definition of a logarithm to prove .
 A By the definition means . B By the definition means . C By the definition means .

21.

Find the accumulated amount after 3 year(s) if \$6,000 is invested at 8% compounded continuously.
 A \$7,609.45 B \$7,621.42 C \$7,591.91 D \$7,627.49

22.

Find the interest rate needed for an investment of \$5,000 to grow to an amount of \$7,000 in 4 year(s) if interest is compounded continuously.
 A 8.55% per year B 8.69% per year C 8.41% per year D 8.62% per year E 8.48% per year

23.

How long will it take an investment of \$7,000 to double if the investment earns interest at the rate of 7% compounded continuously? Round your answer to two decimal places.
 A year(s) B year(s) C year(s) D year(s) E year(s)

24.

Find the present value of \$57,939 due in 6 year(s) at an interest rate of 9% / year compounded continuously. Round your answer to the nearest integer.
 A \$33,764 B \$34,165 C \$33,766 D \$34,547

25.

A condominium complex was purchased by a group of private investors for \$1.5 million and sold 5 year(s) later for \$3.7 million. Find the annual rate of return (compounded continuously) on their investment.
 A 18.90% B 18.47% C 18.06% D 18.19%

26.

Find the derivative of the function.

 A B C D

27.

Find the derivative of the function.

 A B C D

28.

Find the derivative of the function.

 A B C D

29.

Find the derivative of the function.

 A B C D

30.

Find the derivative of the function.

 A B C D

31.

Find the derivative of the function.

 A B C D

32.

Find the derivative of the function.

 A B C D E

33.

Find the second derivative of the function.

 A B C D

34.

Determine the intervals where the function is decreasing.
 A B C D

35.

Determine the intervals of concavity for the function.

 A Concave downward on Concave upward on B Concave downward on Concave upward on C Concave downward on D Concave downward on Concave upward on E Concave downward on Concave upward on

36.

Use the curve-sketching guideline, to select the graph of the function.

 A C B

37.

Based on data obtained from the Census Bureau, the manager of Plymouth Van Lines estimates that the percent of the total population relocating in year t ( corresponds to the year 1960) may be approximated by the formula  .

Compute , , and .
 A B C D E

38.

The monthly demand for a certain brand of perfume is given by the demand equation    where p denotes the retail unit price (in dollars) and x denotes the quantity (in 1-oz bottles) demanded. Find the rate of change of the price to the nearest hundredth of a cent per bottle when  x =  1,000.
 A The rate of change of the price is - 2.22 cents per bottle. B The rate of change of the price is - 3.62 cents per bottle. C The rate of change of the price is - 2.62 cents per bottle. D The rate of change of the price is 5.24 cents per bottle.

39.

The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by

.

How fast is the price of the commodity changing at ?
 A Increasing at the rate of \$14/wk. B Increasing at the rate of \$19/wk. C Increasing at the rate of \$5/wk. D Decreasing at the rate of \$19/wk. E Decreasing at the rate of \$14/wk.

40.

Find the derivative of the function.

 A B C D

41.

Find the derivative of the function.

 A B C D

42.

Find the derivative of the function.

 A B C D

43.

Find the derivative of the function.

 A B C D

44.

Find the derivative of the function.

 A B C D

45.

Find the derivative of the function.

 A B C D

46.

Find the derivative of the function.

 A B C D

47.

Find the second derivative of the function.

 A B C D

48.

Find an equation of the tangent line to the graph of at the point .
 A B C D

49.

Find the inflection points of the function .
 A B C D There are no inflection points.

50.

Find an equation of the tangent line to the graph of     at its inflection point.
 A B C D E

51.

Given that a quantity Q(t) exhibiting exponential decay is described by the function
where t is measured in years. What is the decay constant? What quantity is present initially?

Complete the table of values. Round your answer to the nearest integer.

 t 0 5 10 20 100 Q ____ ____ ____ ____ ____
 A k =  - 0.01;   Q  =  2,500t      0         5        10        20        100  Q      2,500     2,378    2,262     2,047     920 B k  =  - 0.01;   Q  =  2,500t      0        5        10        20        100  Q      2,500    2,378    2,207     2,047     925 C k  =  2,500;   Q  =  - 2,500t     0         5        10        20        100   Q     2,500     2,489    2,262     2,058     920 D k  =  2,500;   Q  =  - 2,500t     0          5        10       20        100  Q     2,500     2,489    2,207     2,058     925

52.

A certain piece of machinery was purchased 4 year(s) ago by Garland Mills for \$400,000. Its present resale value is \$256,000. Assuming that the machine's resale value decreases exponentially, what will it be 2 year(s) from now?
 A The resale value of the machinery will be \$204,800 B The resale value of the machinery will be \$204,789 C The resale value of the machinery will be \$204,911 D The resale value of the machinery will be \$203,689

53.

The radioactive element polonium decays according to the law    where is the initial amount and the time t is measured in days. If the amount of polonium left after 560 days is 40 mg, what was the initial amount present?
 A The initial amount was 642 mg B The initial amount was 629 mg C The initial amount was 635 mg D The initial amount was 640 mg

54.

Wood deposits recovered from an archeological site contain 25% of the carbon 14 they originally contained. How long ago did the tree from which the wood was obtained die? Hint: the decay constant k for carbon 14 is equal to 0.00012.
 A The tree died 13,084 year(s) ago. B The tree died 10,429 year(s) ago. C The tree died 8,096 year(s) ago. D The tree died 11,552 year(s) ago.

55.

The percent of a certain brand of computer chips that will fail after t years of use is estimated to be

.

What percent of this brand of computer chips are expected to be usable after 3 years?
 A 52.6% B 46.9% C 45.5% D 33.7%

56.

During a flu epidemic, the number of children in the Woodbridge Community School System who contracted influenza after t days was given by  .

How many children were stricken by the flu after the first day? How many children had the flu after 10 days? How many children eventually contracted the disease?
 A 13 children were stricken by the flu after the first day; 1,264 children had the flu after 10 days; 883 children eventually contracted the disease B 15 children were stricken by the flu after the first day; 1,125 children had the flu after 10 days; 1,354 children eventually contracted the disease C 13 children were stricken by the flu after the first day; 1,125 children had the flu after 10 days; 1,200 children eventually contracted the disease D 10 children were stricken by the flu after the first day; 1,264 children had the flu after 10 days; 1,200 children eventually contracted the disease

57.

Suppose a radioactive substance decays according to the formula  .  How long will it take for the substance to decay to half the original amount?
 A It will take 5,281 years for the substance to decay to half the original amount. B It will take 5,170 years for the substance to decay to half the original amount. C It will take 5,626 years for the substance to decay to half the original amount. D It will take 40 years for the substance to decay to half the original amount.

Numeric Response

58.

Evaluate the expression.

= __________

59.

Evaluate the expression.

=  __________

60.

Solve the equation for x.

__________

61.

Find the present value of \$58,669 due in 5 year(s) at an interest rate of 7% / year compounded continuously. Round your answer to the nearest dollar.

\$__________

62.

Find the derivative of the function.

63.

Find the derivative of the function.

64.

Find the second derivative of the function.

65.

Find the derivative of the function.