ALGEBRA 2
Name ___________________________ Date ________________ Per ____
PRACTICE TEST CHAPTER 7 Exponential Growth and Decay, e, Logarithms, Exponential and Logarithmic Equations
4-FUNCTION or NO CALCULATOR PART (pages 1 and 2)
m=
n
Product Property
logb mn =
Quotient Property
logb
Power Property
logb mn =
Change of Base
logc a =
1) Expand the expression.
a) log3 3xy
b) ln 10xy3
c) log 5
53 x
y4
d) ln
3y
x5
2) Condense the expression.
a)
3log7 4 + log7 6
b) loga 2x + 3 loga x – 4 loga y
c)
1
ln x  3 ln y
2
3) Use log 4 ≈ 0.6 and log 7 ≈ 0.84 to evaluate the logarithm. Only use the +, -, ÷, × buttons on your calculator.
Hint: 2 is the square root of 4.
a)
log28
b) log
1
4
x 7
4) Graph the parent graph and then y = 2  3 + 6.
c) log4 7
2
70
x
5) Graph the parent graph and then y = e  5 (e≈____)
Parent graph:
Parent graph:
second graph
Growth or decay?
second graph
Growth or decay?
Asymptote: _________
d) log 7
New Asymptote: ______
1
Growth versus Decay:
a) How do you know an exponential function is growth when you look at it? _________________________________
_______________________________________________________________________________________
b) How do you know an exponential function is decay when you look at it?
____________________________
_______________________________________________________________________________________
c) If an exponent is negative and the base is 5, is the function growth or decay? Explain. ______________________
_______________________________________________________________________________________
8) Solve for x. (4-function or mental math.)
a) log 3
1
=x
9
e) log 8 16  3x
b) log 1 8 = x
c) log 3 9 = x
d) f) log 100 = x
2
1
x
16
4
5
g) log 3 3  x
f) log 1
9) Simplify using the inverse properties.
x
7 x
a) log 5 5
b) log 5 125
c) log 2 64 x
10) Find the inverse.
a) y  (0.4) x7
b) y  6 log 1/ 3  4 x   7
e) y  log 9 x  7
f) y  log 6 5 x  4  2
9
h) log 7 49  x
d) e ln x
e) 12log12 x
c) y  log 2 x  3
2
SCIENTIFIC or GRAPHING CALCULATOR PART (pages 3 and 4)
11) (7.6B) Solve the equations.
a) log3 (18x + 7) = log3 (3x + 38)
b) 5 ln x = 35
c) log2(x + 33) = 5
d) 3 log8 (2x+6) + 8 = 10
e) log4 x + log4 (x + 6) = 2
f) 72x-3 – 4 = 14
11 x
g) 3e
3-x
= 15
h) 5(6)
-4x
+1=9
i) 36
5 x 1
1
 
6
j) Which of the above problems have the same answer? ______________________________________
MEMORIZE: Compound Interest formula
MEMORIZE: Continual Compound Interest formula
13) You deposit $1500 in an account that pays 7% annual interest. Find the balance after 2 years if the interest is
compounded:
a) Weekly
b) Monthly
c) Continuously
3
14) You deposited $700 in an account that pays 2.75% annual interest. How long does it take the balance to reach
$1500 if the interest is compounded:
a) Quarterly
b) Daily
c) continuously
INCREASE / DECREASE:
15) In 1998, there were 29,670,000 internet hosts. During the next few years, the number of hosts increased by 39%
each year.
a) Write an exponential growth model giving the number h (in millions) of hosts t years after 1998.
b)
About how many hosts were there in 2003?
c) How long would it take to reach 60,000,000 hosts?
17) You buy a new stereo for $1300 and are able to sell it 4 years later for $275. Assume that the resale value of the
stereo decays exponentially with time.
a) First, determine the decay factor.
b)
Write an equation giving the stereo’s resale value V (in dollars) as a function of the time t (in years) since you
bought it.
4