Download REVIEW - AFM Exp Logs Test

AFM
EXPONENTS AND LOGS TEST REVIEW
Name ________________________________
Date ______________ Per ______________
Show your work on a separate sheet of paper. Circle or box your answers.
VOCABULARY
Domain
Common Log
Range
Natural Log
Asymptote
Exponential Function
FUNCTIONS
1. Is 𝑦 = 5(1.2)𝑥 exponential growth or decay?
Justify your response.
NATURAL LOGS & e
Sketch the graph on graph paper. State the
domain, range, intercepts, asymptotes, end
behavior, and transformation.
15.  4e 2 x  15  7
2. 𝑓(𝑥) = 3(2)𝑥−1 + 4
3. 𝑓(𝑥) = log 3 (𝑥 + 1) − 2
Logarithm
Principal
14. ln x 4  5
16. ln x  ln 4x  10
17. 𝑒 𝑥 ∙ 𝑒 4𝑥 = 7
EXPONENTIAL EQUATIONS
EXPONENTIAL GROWTH & DECAY
4. Solve: 252 x  125 x  2
18. A radioactive substance has a half-life of 26
years. Find the rate of decay.
5. Solve: 2187 x 9  813 x  7
LOGS
6. Write 46  4096 in log form.
7. Write log 9 27 
3
in exponential form.
2
Solve for x.
8. log 2 x 6  5
9.
20. In a laboratory, an organism grows from 100
to 250 in 8 hours. What is the hourly growth
rate?
21. John invests $3,000 in a savings account that
has a 3.25% annual interest rate. What will
the account balance be if he leaves the money
in the account for 12 years, without making
any withdrawals or deposits?
34 x  33 x
10. log 5 4 x  1  log 5 3x 2

19. A current census shows that the population of
a city is 3.5 million, and the population is
growing at a constant rate of 1.1%. Find the
population of the city in 30 years.

2
11. log 2 9 x 5  2 log 2 x  1
22. A computer system depreciates at an average
rate of 4% per month. If the value of the
computer system was originally $12,000, in
how many months is it worth $7350?
x 3
12. 2  5
13. log 6 48  log 6
16
 log 6 5  log 6 5 x
5
23. A music store sold 200 guitars in 2007. The
store sold 180 guitars in 2008. The number of
guitars that the store sells is decreasing
exponentially. If this trend continues, how
many guitars will the store sell in 2012?