Math 3201
Chapter 6 Test Review
1.
2.
3.
Name_____________
Which is the y-intercept of y  3(1.45) x ?
(0, 0)
(0,1)
(A)
(B)
(C)
(0,1.45)
Which function produces a decreasing exponential curve?
x
x
y   12 
(A)
(B)
(C) y   32 
y  2x 1
(D)
(0,3)
(D)
y  3(1.8) x
The graph of y  b x is shown. What value best represents ‘b’?
(A)
3
5
(B)
3
1
(C)
3
(D)
3
y
x
16
4
8
12
– 4
1– 2
2
1
4.
Which equation best models this graph?
y
(A)
y  4x
(B)
y  2  4
x
(C)
y  4  12 
x
(D)
y  4  2
x
16
2
12
8
4
– 2
– 1
1
2 x
– 4
5.
The graphs of y  b x and y  a  b x are shown. What value best represents a?
(A)
(B)
(C)
(D)
2
 12
y
y = b
x
y = ab
x
1
2
2
x
6– 3
3
3– 6
6
3
6.
Which equation best represents the graph shown?
y
6
7.
(A)
y   13 
x
(B)
y   3
x
(C)
y  3  13 
x
(D)
y  3  3
x
– 6
(C)
(D)
3
x
y
2
 12
1
2
x
2
Which represents a decreasing exponential function?
𝑥
𝑥
(A)
𝑦 = (14)
(B)
𝑦 = (54)
(C)
𝑦 = 14(5)𝑥
(D)
𝑦 = (4)𝑥
5– 5
1
2
3
4
1
2
3
4
2– 4
4
2
Which represents an increasing exponential function?
y
– 4
5– 5
1
2
3
4
1
2
3
4
2– 4
4
2
y
5
4
3
2
1
(A)
– 2– 1
– 2
– 3
– 4
– 5
5
4
3
2
1
(B)
2
4
– 4
– 2– 1
– 2
1– 4
2
3
4
5
5
1
2
3
– 3
4– 4
2
2
– 4
– 5
x
2
4
y
– 4
5
4
3
2
1
(D)
– 2– 1
– 2
– 3
– 4
– 5
x
y
5
4
3
2
1
(C)
10.
6
– 3
5– 5
1
2
3
4
1
2
3
4
2– 4
4
2
9.
– 3
Given the graph of y  a  b x shown, what value best represents ‘b’?
(A)
(B)
8.
3
2
4
– 4
x
– 2– 1
– 2
– 3
– 4
– 5
2
4
x
Which graph represents y   32  ?
x
(A)
y
(B)
x
y
(C)
x
y
(D)
x
y
x
11.
Which graph represents an exponential function f ( x)  ab x with b  23 ?
y
(A)
y
(B)
18.
19.
20.
y   54 
(B)
x
(C) y  1.4 
x
y   5.4 
(D)
x
 y | y  0, y  R
 y | y  0, y  R
(D)
 y | y  0, y  R
 y | y  0, y  R
(B)
(D)
{𝑦|𝑦 < 0; 𝑦𝜖𝑅}
{𝑦|𝑦 < 4; 𝑦𝜖𝑅}
(B)
What is the domain of y   14  ?
x
(C)
17.
x
What is the range of y  4 x ?
{𝑦|𝑦 > 0; 𝑦𝜖𝑅}
(A)
{𝑦|𝑦 > 4; 𝑦𝜖𝑅}
(C)
(A)
16.
x
x
(C)
15.
y   54 
What is the range of y   12  ?
(A)
14.
x
Which produces a decreasing exponential curve?
(A)
13.
y
(D)
x
x
12.
y
(C)
x | x  R
x | x  14 , x  R
(D)
x | x  0, x  R
x | x  14 , x  R
(B)
Solve for x:
 73
(A)
3x 3  34 x 10
(B)
 75
(C)
13
5
(D)
13
3
Solve for x:
(A)
 13
23 x5  16
(B)
1
(C)
3
(D)
13
3
Solve: 4 x1  161
(A)
3
(B)
2
(C)
1
(D)
2
Solve: 8 x  32 .
3
(A)
5
(B)
5
3
(C)
4
(D)
24
Solve: 93 x 1  81 x 1
3
(A)
(B)
10
2
5
(C)
1
2
(D)
3
5
21.
22.
Solve: 2 x  32 .
1
(A)
5
Solve: 333 x   19 
(A)
23.
24.
1
2
Solve: 43x1  2 .
1
(A)
 12
Solve: 53 x 
(A)
25.
2 x
 32
1
25
(B)
2
5
(C)
5
2
(D)
5
(B)
1
5
(C)
5
7
(D)
7
5
(B)
 14
(C)
1
6
(D)
5
12
(B)
 23
(C)
2
3
(D)
3
2
.
.
For the data, (0, 3), (1, 7), (2, 10), (3, 24), (4, 50), (5, 95), the exponential regression
curve of best fit was determined to be y  3.0465(1.988) x . Determine the value of
y when x = 7.
(A)
150
(B)
374
(C)
492
(D)
500
t
26.
27.
The population of caribou in Bay St. George is modeled by the function P(t )  50(2) 3
where P(t) represents the number of caribou and t represents the time in years after the
initial count. How much time will it take for the number of caribou to reach 6400?
(A)
9 yrs
(B)
12 yrs
(C)
18 yrs
(D)
21 yrs
Which is true for the following table of values?
x( yr ) 0 3 6 9
y (amt ) 10 20 40 80
(A)
(B)
(C)
(D)
initial amount is 10, the amount doubles every 3 years
initial amout is 10, the amount triples every 2 years
initial amount is 20, the amount doubles every 3 years
initial amount is 20, the amount triples every 2 years
The function that models the decay of carbon-14 is A(t )  100  12  5730 , where A(t) is the
number of grams of carbon-14 present at time t, in years. Which statement is true?
(A)
The amount of carbon-14 doubles every 5730 years.
(B)
There are 50 grams of carbon-14 present initially.
(C)
14 g will be present after 50 years.
(D)
50 g of carbon-14 will be present after 5730 years.
t
28.
29.
Jacie invests $2000 into an account that pays 8% interest a year compounded semiannually for the next 4 years. How many compounding periods will there be in the 4 year
time frame?
(A)
4
(B)
8
(C)
12
(D)
16
30.
Ken invests $2000 into an account that earns 8% simple interest awarded annually. How
much money will be in his account at the end of 5 years?
(A)
$2800
(B)
$2938.66
(C)
$3200
(D)
$3537.48
Constucted Response. Show all workings.
31.
Explain how you could use the graph to solve the equation 4  2(3) x3  2
32.
Explain how you know that each relation represents an exponential function. Is the
function increasing or decreasing?
x 0 1 2
3
(A)
(B)
y 80 20 5 1.25
33.
Algebraically solve for x:
3
(A)
42𝑥+3 = √16
(C)
10(103 )𝑥−1 = 1 000 000
(B)
(D)
2(8𝑥+1 )3 = 64
 14 
3 x
 64 x 1
34.
The population, P, of a bacteria culture is described by the function
t
P(t )  320(2)15 where t is time in minutes.
(A)
How long, in minutes, will it take for the bacteria population to double?
(B)
How many bacteria will there be after 3 hours?
(C)
How many minutes will it take for the population to 20480?
35.
The remaining amount of a sample of radioactive tin-117 can be modeled by the function
𝑡
1 14
𝐴𝑜 (2)
𝐴(𝑡) =
where 𝐴(𝑡) represents the number of milligrams of tin-117 remaining
after 𝑡 days. If there was 100 milligrams of tin-117 present initially, determine the
amount remaining after four weeks?
36.
A principal of $4500 was invested for 6 years in an account in which 4% compound
interest was compounded quarterly. How much money was in the account at the end
of 6 years?
37.
Stella has inherited $5000 from her grandfather. She plans to invest it into an account
until she can decide what to do with the money. She has 2 options.
Option 1: 6% interest a year compounded monthly for a 3 year period.
Option 2: 6.5% interest a year compounded semi-annually for a 3 year period.
Write a function that models each situation. Which option should Stella choose?
Support your answer with calculations.
38.
Mr. Alexander performed exponential regression
using some data values. The resulting curve and
equation of best fit are shown. Use the curve of best fit
or the equation to determine the value of y when x = 1.5.
Answers:
1.
D
2.
B
3.
C
4.
D
5.
C
6.
C
7.
C
8.
A
9.
A
10.
B
11.
D
12.
A
13.
A
14.
A
15.
A
16.
D
17.
A
18.
A
19.
B
20.
D
21.
C
22.
D
23.
B
24.
B
25.
B
26.
D
27.
A
28.
D
29.
B
30.
B
31.
look at the graph and determine the value of x when y = 4. The answer is x = 3.
32.
(A)
It’s exponential since each y-value is divided by 4 to get the next y value. It’s a
decreasing function.
x
(B)
It’s exponential since the equation, y  0.5(4) x is in the form y  a  b  . It’s an
increasing function since the value of b (4) is bigger than 1.
x   94
33.
(A)
x=  76
(B)
(C)
(D)
x = -3
x  83
34.
35.
36.
37.
38.
 
(A)
15 mins
(B)
P(t )  320(2) 15  1310720
25 mg
$5713.81
Option 1 $5983.40 Option 2 $6057.74 #2
From graph or equation, when x = 1.5, y = 4
180
(C)
t =90 mins