Download 6 Unit Exponentials Public Exam Review File

Chapter 6: Exponentials
Math 3201
Public Exam Review
Write the letter of the correct response in the space provided to the left
1.
_____
Which statement best describes the exponential function f(x) = 3  1  ?
 4
A. Increasing function; y-intercept 3 B. Decreasing function; y-intercept 3
C. Increasing function y-intercept ¾ D. Decreasing function; y-intercept ¾
2.
_____
Which is an increasing exponential function?
x
A.
C.
f(x) = 5  1 
2 3
x
3
f(x) = (1)
2
x
B.
f(x) = 1.5(0.5)
D.
f(x) = 1  5 
3 2
x
x
y
3.
_____
Which exponential function best represents the graph?
A.
B.
C.
D.
6
x
f(x) =  1 
 4
x
f(x) = (4)
x
f(x) = 4  1 
 4
x
f(x) = 4(4)
4
2
x
-2
4.
_____
x
What is the end behavior of the function y = 2  1  ?
 3
A.
C.
5.
_____
Extends from Q1 to Q2
Extends from Q3 to Q4
A.
B.
C.
D.
_____
Extends from Q2 to Q1
Extends from Q4 to Q3
Which statement is true about the table shown below?
x (years)
y (amount)
6.
B.
D.
-3
5
0
10
3
20
6
40
9
80
12
160
An initial amount of 5 doubles every 3 years
An initial amount of 5 triples every 2 years
An initial amount of 10 doubles every 3 years
An initial amount of 10 triples every 2 years
x–2
x–2
= 9 , the graphs of y = 3
To solve the equation 3
and y = 9 were
drawn, as shown below. What is the solution to the equation?
A.
B.
C.
D.
y
0
4
9
there is no solution
10
8
6
4
2
7.
_____
Solve for x: 2
A.
C.
-3
2
3x + 1
=4
2x – 1
-2
B.
D.
-2
3
2
4
6
x
-2
Page 1 of 4
Chapter 6: Exponentials
8.
_____
Solve for x: 9
A.
_____
Public Exam Review
= 3
B.
–3
8
–1
2
C.
9.
2x + 1
Math 3201
D.
–1
4
1
2
The population growth of a strain of bacteria in a Petri dish is modeled by the
t
4
function P(t) = 3000(2) where P(t) represents the number of bacteria after t
hours from the initial count. How long will it take for there to be 12000
bacteria?
A.
C.
10. _____
4 hours
16 hours
a)
c)
8 hours
32 hours
In the bacteria growth in #9 above, how many will be present 6 hours after the
initial count?
A.
C.
11.
B.
D.
4762
48000
B.
D.
8485
192000
Algebraically solve each equation. Show all necessary workings
9
x+1
= (27)
 1 


 216 
2x
2x
4x + 1
=6
b)
d)
4(5)
x–4
– 25 = 75
2x + 1
7 = 49
Page 2 of 4
Chapter 6: Exponentials
12.
Math 3201
Public Exam Review
Small rural water systems are often contaminated with bacteria from animals. The
number of bacteria present in the tank after t days can be modeled by the function
A(t) = 14000(2)
t
4
a)
How many bacteria are initially present?
b)
How many days does it take for the bacteria to double?
c)
Algebraically determine when the number of bacteria will be 224000.
13.
Sharon wants to invest $5600 into an account for 7 years. She has the following
options:
Account #1 has an annual interest rate of 5% compounded quarterly
Account #2 has an annual interest rate of 4% compounded semi-annually
a)
Develop an equation in the form A = P(1 + i) to represent the value of the money
in each account and use it to determine how much money would be in each account
at 7 years.
b)
Which account is the best investment option?
n
Page 3 of 4
Chapter 6: Exponentials
Math 3201
Public Exam Review
14.
The value of a $47000 car depreciates at a rate of 21% every 2 years.
a)
Write an exponential function to describe the value of the car over time (t).
b)
Use the function from part (a) to algebraically determine the value of the car in 15
years.
15.
The value of a $157000 house increases by 12% every 4 years.
a)
Write an exponential function to describe the value of the house over time (t)
b)
Use the function from part (a) to algebraically determine the value of the house in
25 years
Page 4 of 4