Name:
Period:
MU
College Algebra: Expos and Logs Test (4.5 - 4.8)
You must show supporting work for all problems to receive credit. Calculators are required.
In problems 1 - 4, choose the one alternative that best completes the statement or answers the question.
Supporting work/reasoning must be shown in order to receive credit for your answer.
1. What rate of interest compounded annually is required to triple an investment in 12 years?
A.
B.
C.
D.
E.
10.1%
5.5%
7.3%
9.6%
None of the above
1. ________(+2)
2. What is the value of an account in 5 yrs if it starts with $1,500 and earns 4.43% compounded daily?
A.
B.
C.
D.
E.
$1,871.90
$1,868.89
$1,870.88
$1,872.89
None of the above
2. ________(+2)
0.5 h
3. The formula D  7e
can be used to find the number of milligrams D of a certain drug that is in a
patient's bloodstream h hours after the drug has been administered. The drug is to be administered again when
the amount in the bloodstream reaches 3 milligrams. What is the time between injections?
A.
B.
C.
D.
E.
about 0.8 hour
about 2.2 hours
about 1.7 hours
about 1.8 hours
None of the above
3. ________(+2)
4. The half-life of radioactive cobalt is 6.3 years. If a sample presently contains 100 grams of radioactive
cobalt now, how much will be present in 20 years?
A.
B.
C.
D.
E.
10.5 grams
11.1 grams
13.8 grams
12.5 grams
None of the above
4. ________(+2)
5. What does the point (2, 1/3) of the parent function become when transformed by f ( x)  7  log 8  4 x  1?
A. (-1/4, -22/3)
B. (1/4, -20/3)
5. ________(+2)
C. (-8, -22/3)
D. (-8, -20/3)
E. None of the above
In 6 - 8, to receive credit for your answer, you must clearly state all formulas used and show all relevant
algebraic work required to support your answer.
6. Assume your grandparents purchase a $20,000 bond on your fifth birthday to be used for your college
education. The bond value grows at 6% compounded monthly.
a) How much will the bond be worth on your 18th birthday? Round calculation to the nearest dollar.
a) ____________________(+2)
b) How many years will it take for the bond to quadruple in value? Round calculation to one decimal place.
b) ____________________(+2)
c) How much would your grandparents have had to invest initially in order for the bond to be worth $100,000
on your 18th birthday? Round calculation to the nearest dollar.
c) ____________________(+2)
d) If instead, the bond is compounded continuously at 6% , how many years will it take for the bond to triple in
value? Round calculation to one decimal place.
d) ____________________(+2)
7. Assume the average selling price of a home in Fort Collins grows according to uninhibited exponential
growth. If the average selling price of a home was $35,500 in 1979 and it was $250,500 in 2023, what can you
predict the average selling price of a home in Fort Collins will be in the year 2035? Round to nearest dollar.
7. _________________________ (+3)
8. “Bananas Foster” is a dessert served flambe' style at your table featuring banana slices cooked in a vanilla,
brown sugar, and cinnamon cream sauce. Assume the heated banana slices are initially 375 °F and the room
temperature is 70 °F. After 7 minutes, the temperature of the bananas is 250 °F. If you cannot eat the banana
slices until they cool to 135 °F, how many minutes will you have to wait before you can eat your dessert?
Round calculation to one decimal place.
8. _________________________ (+3)
Solve the following exponential equations. Give logarithmic answers in terms of natural log, ln, with reduced
improper fractions within ln. Combine log expressions to single logarithms when applicable for full credit.
9. 32x 1  7 x1
10.
e x  4e  x
1
4
9. _________________ (+5)
10. _________________ (+5)
11. 4 x  2 x4  63  0
12. 82 x 
2 x 3
4
 x 1
32
2
11. _________________ (+5)
12. _________________ (+5)
Solve the following logarithmic equations. Reduce and simplify all answers. No decimal answers will be
accepted.
13. 2 log 3 (x  4)  log 3 6  2
14. ln 4  ln( 5  x )  ln x
13. ______________ (+5)
14. ______________ (+5)
15. log 3 ( x  1)  log 9 9   log 3 (2x  3)
16. 4 log 4 ( x )  log 16 x  9
15. ____________ (+5)
16. ____________ (+5)
17. Write as a sum and/or difference of logarithms. Express all powers as factors and factor completely.


 2x 7 x  4 

ln 
 2 x 2  50 3 




17. ______________________________________________________________________ (+5)