MAT 111 Final Exam
Fall 2013
Name: __________________________________
•
Show all work on test to receive credit.
•
Draw a box around your answer.
•
If solving algebraically, show all steps.
•
If solving graphically, sketch a graph and label the solution.
•
Where appropriate, round correctly to 2 decimal places.
•
200 possible points
Fall 2013
MAT 111 Final Exam
Name: ______________________________
Score: _________/200
Show all work on test to receive credit. Draw a box around your answer. If solving algebraically,
show all steps. If solving graphically, sketch a graph and label the solution(s). Where
appropriate, round correctly to 2 decimal places.
1.
[6 pt.] Solve.
(
3. [8 pt.] Solve.
)
2. [6 pt.] Solve. Find the exact value.
√
4. [8 pt.] Solve the following inequality. Write
the solution in interval notation.
5. [8 pt.] Solve the following inequality. Write
the solution in interval notation.
|
(
)
|
6. [6 pt.] Solve the system of equations.
{
7. [8 pt.] Solve.
8. [8 pt.] Solve algebraically.
(
)
9. [6 pt.] Find all real and complex solutions and
simplify.
11. Sketch the graphs of the following.
(Label all intercepts and asymptotes.)
a. [3 pt.]
b. [3 pt.]
10. [6 pt.] Write the following as a sum and
difference of simple logs (powers as factors).
(
[
)
√
]
y  ex  2
y  log 6 x
12. Starting with the graph of y  f x 
(pictured)
a. [4 pt.] List the transformations necessary
to obtain the new function y  f  x   4 .
b. [4 pt.] Graph the new function (on the
same axes). Label three points.
13. The table below lists the amount of money spent
by five students at the county fair, compared with
the amount of time each student remained at the
fair.
Time at Fair
Total Money Spent
69
57
37
85
90
68
(in minutes)
40
113
120
84
(in dollars)
a. [4 pt.] Using you graphing calculator, decide
whether a linear or exponential model is
more appropriate. Give a reason for your
answer.
14. Given the function ( )
a. [2 pt.] Find the domain of ( )
b. [2 pt.] Find the x-intercepts.
c. [2 pt.] Find the y-intercepts.
b. [4 pt.] Express the model of best fit that
predicts total money spent, M, as a function of
time, t, at the fair.
d. [4 pt.] Locate vertical asymptotes.
e. [2 pt.] Determine horizontal asymptotes.
c. [2 pt.] Using the answer to part (b), estimate
the money spent for someone who was at the
fair for 73 minutes. (to the nearest dollar)
f. [4 pt.] Sketch the graph of ( ) Label all
intercepts and asymptotes.
d. [2 pt.] Given that a student spent $95, what is
the student’s approximate time spent walking
around the fair. (to the nearest minute)
17. Consider
15. Given the function ( )
a. [5 pt.] Find the inverse function
( )
( )
(
) (
) (
)
a. [2 pt.] The end behavior of the graph of
( ) resembles the graph of what power
function?
b. [9 pt.] Find the zeros and their
multiplicities.
Zeros
b. [2 pt.] What is the range of ( )
16. Given ( )
a. [3 pt.] Find (
and ( )
c. [4 pt.] Graph.
√
)( ).
b. [3 pt.] Find the domain of (
interval notation.
)( ) in
Multiplicity Touch or
Cross?
18. Yeast in a sugar solution is growing at a rate
such that 2 grams becomes 5 grams after 23
hours.
a. [4 pt.] Find the growth constant.
19. Given ( )
+2
a. [2 pt.] Use a graphing calculator to sketch
the graph of ( )
b. [2 pt.] Find and label the local maximum
point(s).
b. [2 pt.] Find the exponential growth
function.
c. [2 pt.] Find and label the local minimum
point(s).
d. [4 pt.] On what interval(s) is ( )
decreasing?
c. [4 pt.] How long will it take for the yeast
to double in size?
20. [6 pt.] Find the equation of the line in
slope- intercept form that is perpendicular
to
and passes through the
point ( ).
21. [6 pt.] To celebrate the birth of a new
daughter, Helen invests $6,000 in a college
savings plan to pay for her daughter’s first
year of college. How much will she have
after 18 years of saving if her money is
invested at 6% compounded quarterly?
23. Let
( )
{
a. [4 pt.] Sketch f (x) labeling key
points.
22. [8 pt.] A coffee manufacturer wants to
market a new blend of coffee that will sell for
$4.19 per pound by mixing Folger’s coffee
that sells for $2.75 and Colombian coffee that
sells for $5.00 per pound, respectively. What
amounts of each coffee should be blended to
obtain 100 pounds of the desired mixture?
b. [2 pt.] Find the domain of f (x) . Use
interval notation.
c. [2 pt.] Find the range of f (x) . Use
interval notation.
d. [2 pt.]
( )
e. [2 pt.]
(
)
24. The price P (in dollars) and the quantity x
sold of a certain product obey the revenue
function below.
( )
a. [3 pt.] What quantity x maximize the
revenue?
b. [3 pt.] What is the maximum revenue?
c. [2 pt.] What price should the company
charge to maximize the revenue?