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Chapter 3 Quiz 1 – REVIEW
NON-CALCULATOR PORTION
For the quiz, you should be able to:
Pre-Calculus
1. Write the equation for each graph
B.
A.
2. Write the equation for a given table
y
X
-2
-1
0
1
2





Y
108
36
12
4
4/3

x

1
y  12   or y  12(3)  x
3
x










a. y = 3x
b. y = 4-x or (¼) x
3. Identify whether a function is exponential. If it is, be able to state the initial value and base, and if it is
growth or decay. If it is not exponential, be able to state why it isn’t.
a. 7-3x
b. 3e2x
c. 6(0.23x)
d. 7x – 5
exponential
exponential
exponential
not exponential
initial value = 1
initial value = 3
initial value = 6
exponent is constant or base is variable
base = 7
base = e
base = 0.2
decay
growth
decay
4. Know the properties of logs
a. log10 = 1
b. eln22= 22
2
11
c. log8 11 64 =
d. log1 = 0
5. Be able to describe how to transform the graph of an exponential function and sketch the graph.
f(x) = 2x
g(x) = 3(2-2x) – 1
y


Vertical stretch 3
Horizontal shrink 1/2
Reflect over y-axis
Down 1




Start points (0,1) and (1,2)

Key points become (- ½ , 5) and (0,2)
Horizontal asymptote at y= -1

x















CALCULATOR PORTION
6. Be able to solve equations.
a. 10x = 23,587
log1023587 = x
x = 4.373
b. lnx = 5.29
e5.29 = x
x = 198.343
7. Be able to solve problems with logistic models.
Four students start a rumor where the number of students who have heard the rumor by the end of t days is
modeled by:
1200
S (t ) 
1  39e0.9t
a. How many students have heard the rumor by the end of day 0?
S(0) = 12000/(1+39) = 1200/40 = 30 students
b. How long does it take for 1000 students to hear the rumor?
Put equation into y1 and 1000 into y2, find point of intersection. Answer: 5.859 days
c. What is the maximum number of students who can hear the rumor?
1200 (just the numerator, remember it represents the limit of growth)
8. Be able to solve word problems with log models.
The time t, in minutes, for a small plane to climb to an altitude of h feet is given by
18, 000
t  50 log
18, 000  h
Find the time for the plane to climb to an altitude of 4,000 feet.
Substitute 4000 in for h and calculate
t = 5.457 minutes