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


1.

Evaluate the expression.


2.

Evaluate the expression.


3.

Simplify the expression.


4.

Simplify the expression.


5.

Solve the equation for x.
A  x = 2  B  x = 16  C  x
= 8  D  x = 7 


6.

Solve the equation for x.


7.

Solve the equation for x.


8.

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


9.

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


10.

Sketch the graphs of the functions on the same axes.


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?


12.

Express the equation in logarithmic form.


13.

Express the equation in logarithmic form.


14.

Sketch the graph of the equation.


15.

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


16.

Use logarithms to solve the equation for t.


17.

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


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 70ft 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 ? Please round the answer to two
decimal places.
A  sec  B 
sec  C  sec  D 
sec  E  sec 


20.

Use the definition of a logarithm to prove .


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.


27.

Find the derivative of the function.


28.

Find the derivative of the function.


29.

Find the derivative of the function.


30.

Find the derivative of the function.


31.

Find the derivative of the function.


32.

Find the derivative of the function.


33.

Find the second derivative of the function.


34.

Determine the intervals where the function is
decreasing.


35.

Determine the intervals of concavity for the function.


36.

Use the curvesketching guideline, to select the graph of the function.


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 .


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 1oz 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.


41.

Find the derivative of the function.


42.

Find the derivative of the function.


43.

Find the derivative of the function.


44.

Find the derivative of the function.


45.

Find the derivative of the function.


46.

Find the derivative of the function.


47.

Find the second derivative of the function.


48.

Find an equation of the tangent line to the graph of at the point
.


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.


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


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.
$__________

Short Answer


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.
