ALGEBRA II
UNIT ELF – EXPONENTIAL
WITH
AND
TRIGONOMETRY: FINAL EXAM REVIEW 2015
LOGARITHMIC FUNCTIONS
DUE DATE: ______________
Directions: Complete ALL questions for full credit. Do all work on notebook paper
and/or graph paper.
ELF 1: Exponential Growth and Decay




Graphs of exponential growth and decay functions
Applications of exponential growth and decay
Applications of compound interest
Natural base e and continuous compounding
ELF 2: Solving Exponential Equations

Applying exponent rules to solve exponential equations
ELF 3: Logarithmic Functions




Natural log
Writing in logarithmic and exponential form
Evaluating logs
Change of Base
ELF 4: Solving Logarithmic Equations

Solving equations with logs
ELF 5: Graphing Exponential and Logarithmic Functions



Graphing exponential and logarithmic functions
Identifying asymptotes
Transformations of exponential and logarithmic graphs
ELF 6: Applications

Applications using logs and exponential functions
MD/PH/CR/RS 6-15
Page 1 of 4
ALGEBRA II
TRIGONOMETRY: FINAL EXAM REVIEW 2015
WITH
PROBLEM SET
1)
Write in logarithmic form.
a)
72 = 49
2)
Write in exponential form.
a)
log6 216 = 3
b)
b)
34 = 81
c)
641/3 = 4
log 100000 = 5
c)
log5 x = 6
3)
Evaluate. (NO Calculators!!)
a)
æ 1 ö
log 4 çç ÷÷ è 64 ø
b)
log1/11 11
c)
log 75 1
d)
log 625 5
e)
log 3 27 3
f)
log 4 32
g)
log 8 2
h)
log13 - 4
i)
log 6 65
4)
Solve each of the following logarithmic equations.
5)
a)
log (5x) = 4
b)
log4 x= -1.5
c)
logx 5 = 1/2
d)
log 4 (x2 – 17) = 3
e)
2 logm (x + 1) - logm 4 = 0
f)
log 3 (a2 – 15) = log
g)
-4 ln 2x = -26
h)
3e-3x + 4 = 6
3
2a
Solve each exponential equation.
a)
82+x = 2
b)
2x = 13
c)
3x+2 + 1 = 15
d)
8(3x) - 1 = 22
MD/PH/CR/RS 6-15
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ALGEBRA II
WITH
TRIGONOMETRY: FINAL EXAM REVIEW 2015
6)
Graph each function. Identify the transformation (if any), the asymptote, and the
x- or y-intercept.
a)
f(x) = 2x-1
c)
æ1ö
f(x) = çç ÷÷
è2ø
b)
f(x) = log x
3
x-2
MD/PH/CR/RS 6-15
-1
d)
f(x) = log (x + 1) - 2
2
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ALGEBRA II
WITH
TRIGONOMETRY: FINAL EXAM REVIEW 2015
Applications
EXPONENTIAL GROWTH FUNCTION
EXPONENTIAL DECAY FUNCTION
f(t) = aekt
f(t) = ae-kt
Formulas: y = A(1 + r)t
y = A(1 - r)t
r
A = P (1 + )nt
n
A = Pert
7)
The population of Winnemucca, Nevada, can be modeled by P = 6191 (1.04)t where t
is the number of years since 1990. What was the population in 1990? By what
percent did the population increase each year? What was the expected population
in 1998?
8)
You have inherited land that was purchased for $30,000 in 1960. The value of the
land increased by approximately 5% per year. What is the approximate value of the
land in 2015?
9)
Wade deposits $1600 in a bank account. Find the balance after 3 years for each of
the following situations:
a)
b)
c)
The account pays 2.5% annual interest compounded quarterly.
The account pays 4% annual interest compounded yearly.
The account pays 2.75% annual interest compounded continuously.
10)
Rose buys a new computer for $2100. The computer decreases by 35% annually.
When will the computer have a value of approximately $600?
11)
Strontium-90 is a radioactive material that decays according to the equation:
A  Ao e 0.0244t , where Ao is the initial amount present and A is the amount present at
time t in years.
a)
b)
What is the half-life of strontium-90?
Determine how long it takes for 100 grams of strontium-90 to decay to 10
grams.
MD/PH/CR/RS 6-15
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