Pre-Calculus Honors
Unit 2 Part B Review Packet
Name ____________________________
Date _______________ Period ______
Mrs. Iverson
Part 1: No Calculator
1. Match each graph to one of the equations using the letters a – d. y
 log
10 x ______________
b) a) y
 log
10 x

3 ___________
c) d) y
 
10 x ___________ y
 log (
10 x

3) __________
2. Graph y

4 x

3 
2 by hand.
Intercept(s): ___________
Domain: __________
Extra point: __________
Asymptote(s): ___________ Increasing or Decreasing?
Range: __________
Describe transformation: _____________________________
3. Graph y
 log ( x
 
2
Intercept(s): ___________
Domain: __________
Extra point: __________
Asymptote(s): ___________ Increasing or Decreasing?
Range: __________
Describe transformation: _____________________________
4) Find the intercept & asymptote of y
  log ( x

2) .

5) Simplify each expression using the properties of exponents or logarithms. SHOW ALL WORK.
A. log 1
12
(1/ 2) B.
log 16 ln
2
 e
3 C. log
4
1
64
D. log 1
(1/ 2) E.  e
3 F. log 6
4 
5ln e
6) Expand and simplify if possible:
A. log 2 x
B. ln
2 x y 2
1 e
7 x
C. log
6
4 x
2 
9
7) Write each as a single logarithm. (condense)
A.
 
2 x
 
3log
2 y
B. (2 log 6 4 log ) log( a

1)
8) Solve or simplify. SHOW ALL WORK
A. log
5 x

3 B. 16 x 
32 C. 243

3
9 x

4

D. 5 x
 ln e
3 x 
16 E. log 6
6
4 
5 ln e F. log
7 x
 log 5
7

3
G. x log 3
10
 log 81
10
H. 3 e
2 x 
4 e x  
0
Part 2: Calculator.
#9 – 14: Solve. Round all FINAL answers to the nearest thousandths when necessary.
9. 5
3 x 
18 10. 2ln 4 x

15 11. 4 e
3 x 
84
12. 14 2 e x 
3 13.
 x

0 14. log
10 x
 log (2
10 x
 
Equations you may need: A

Pe rt and
A

P


  r n
15. The demand equation for an IPod is modeled by


 nt p
  e 0.006
x
. Find the demand x for a price
(p) of $200.
16. Jack deposits $30,000 into an account compounded continuously for 12 years and 3 months. What must the interest rate be in order for Jack to make double his money in this time?

17. A) If a credit union pays 6.5% annual interest compounded daily, what will a deposit of $2300 be worth after 5 years and 4 months?
B) How much interest would be compounded if the initial amount was compounded quarterly?
18. The population P (in thousands) of Colorado Springs, Colorado is given by P

361 e kt
where t

0 represents the year 2000. In 1980, the population was 215,000. Predict the population in the year
2020.
19. The number N of bacteria in a culture is given by the model
N

240 when 5
N

100 e kt where t is the time (in hours). If t

, estimate the time required for the population to double in size.
20. Georgia wants to buy an SUV that has a value of $28,000 new and is $20,000 after 3 years.
A) Find the linear model V = mt + b .
What does the slope mean in the context of this problem?
B) Find the exponential model V
 ae kt
.
C) Use each model to find the value of the car after 8 years. If Georgia saves $11,000 for the 8 year old car, will she have enough money to buy the car?

21. In a typing class, the average number of words per minute, N, after t weeks of lessons was found to be modeled by N

157
 e

0.12
t
. Find the number of weeks necessary to type 50 words per minute.
CHALLENGE:
22. Solve for a when y= e+2: y

10
1

 e 3 e a
2
*23. Solve 7 x 2
= 28 . Round your answer to the nearest hundredth, if necessary.