Name: Period:
You must show supporting work on all problems to receive credit. Calculators are required.
I

P r t A

P
0
1 r n nt
A

P
0 e rt
A

A
0 e kt
  

T

 
0

T
 e kt
In problems 1 - 5, 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. (+2 ea)
1.
Evaluate by using properties of logarithms. ( 3 ln 6

2 ln 4 )
 ln 48
1. 1. ______
A.
ln 3
B.
C.
D.
E.
ln 36 ln 12 ln 72
None of the above
2. The half-life of radioactive cobalt is 4.9 years. If a sample presently contains 120 grams of radioactive cobalt now, how much will be present in 25 years?
2. ______
A.
B.
C.
D.
E.
57.2 grams
58.3 grams
61.7 grams
60.5 grams
None of the above
3. The formula D

8 e

0 .
6 h
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 5 milligrams. What is the time between injections?
A.
B.
C.
D.
about 0.8 of an hour about 1.5 hours about 0.7 of an hour about 1.1 hours
3. ______
E.
None of the above
4.
The logistic model
95.4993
1+0.0405𝑒 0.1968𝑡 represents the percentage of households that do NOT own a personal computer t years since 1984. What percentage of households owned a personal computer in 1984?
A.
95.4993%
B.
4.05%
4. ______
C.
D.
A.
19.68%
4.5007%
None of the above
5.
What is the effective rate of interest for 10% compounded daily?
A. 10.81%
B. 10.76%
C. 10.25%
D. 10.52%
E. None of the above
5. ________
(+2)
C

Solve the following logarithmic equations algebraically. No decimal answers will be accepted.
6. 2 log
4
( x

3 )
 log
4
8

2 7. ln 12
 ln( 7
 x )
 ln x
6.
__________
(+5)
7.
__________
(+5)
8. log
5
 x

2

 log
5
( 2 x

1 )
 log 10 9. 3 log
5 x
 log
25 x

14
8.
__________
(+5)
9.
__________
(+5)

Solve the following exponential equations algebraically. If applicable, give logarithmic answers in terms of natural log, ln . Combine log expressions to a single logarithm when applicable.
10. 5
3 x 
4
3 x

1
11. e x 
6 e
 x
5

1 10.
_________________
(+5)
12. 9 x 
3 x

2 
20

0 13. 8 x 
4 x 
2 x

1 
32

1
(Remember you need a common base!)
11.
_________________
(+5)
12.
_________________
(+5)
13.
_________________
(+5)

14.
Write as a sum and/or difference of logarithms. Express all powers as factors, factor completely, and combine like terms. ln



( 3 x
 x

2 
6 )
 x
4 x
2

2

3
1






14. ______________________________________________________________________
(+5)
In 15 - 17, to receive credit for your answer, you must clearly state all work/formulas used and show all work required to support your answer.
15. 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 $25,600 at the start of 1976 and it was $226,400 at the start of 2007, what can you predict the average selling price of a home in Fort Collins will be in the year 2030?
Round to the nearest dollar.
15.
_____________________
(+3)

16. Assume your parents invest $15,000 into a stock fund when you are born to be used for your college education. The investment does well, on average, and the value grows at 6% compounded monthly. a) How much will the investment be worth on your 18 th
birthday? Round to the nearest dollar. a) ______________
(+2) b) How many years will it take for the bond to double in value? Round to one decimal place. b) _____________
(+2) c) How much would you have had to invest initially in order for the investment to be worth $50,000 on your
18 th
birthday? Round to the nearest dollar. c) ______________
(+2) d) If instead, the investment is compounded continuously at 6%, how many years will it take for the investment to triple in value? Round to one decimal place.
d) _____________
(+2)
17.
“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 350 °F and the room temperature is 65 °F. After 5 minutes, the temperature of the bananas is 225 °F. If you cannot eat the banana slices until they cool to 150 °F, how many minutes will you have to wait before you can eat your dessert?
Round answer to the nearest minute.
17.
_____________________
(+3)