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Exponential Review

Total questions: 80

Worksheet time: 6hrs 22mins

Name
Class
Date
1.
What is the growth or decay rate for the following equation?
y = 2.5(1.15)x
a)
-15% decay
b)
115% growth
c)
15% growth
d)
25% growth
2.
What is the growth or decay rate for the following equation?
y = 1/3(0.7)x
a)
7% decay
b)
70% decay
c)
30% growth
d)
30% decay
3.
A population has a growth/decay factor of 1.045 What is happening to the population?
a)
It grows at a rate of 45%
b)
It grows at a rate of 4.5%
c)
It dies at a rate of 45%
d)
It dies at a rate of 1045%
4.
An adult takes 800 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%. How much ibuprofen is left after 6 hours? 
a)
101
b)
102
c)
103
d)
104
5.
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 the year 2011?
a)
$344,022
b)
$31,500
c)
$15,000
d)
$28,500
6.
The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.
a)
y=1400(1.09)x
b)
y=1.09(1400)x
c)
y=1400(.91)x
d)
y=1.09x
7.
What is the y-intercept of the function?
a)
2
b)
3
c)
1
d)
-2
8.
The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)t where t is the number of years since 1990. What percent did the population increase each year?
a)
4%
b)
It doesn't say
c)
I don't know
d)
400%
9.
Is this exponential growth or decay?
a)
Growth
b)
Decay
10.
What type of function is y = 7(5/4)x?
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None of the above
11.
Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.
a)
y=5000(0.7)x
b)
y=30(5000)x
c)
y=5000(1.3)x
d)
y=5000xx
12.

What is the asymptote of the function y=5(0.5)x ?

a)

y=5

b)

y=0.5

c)

y=0

d)

y=1

13.
Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.
a)
y=6(0.14)x
b)
y=6(1+14)x
c)
y=6(1.14)x
d)
y=6(0.86)x
14.
Which of the following functions shows an initial amount of $15 and an increase of 35% each year?
a)
y = 15(35)x
b)
y = 15(1.35)x
c)
y = 15(0.35)x
d)
y = 35(1.15)x
15.
Identify the y-intercept (initial value) in the function f(x)=13(.27)x
a)
(.27)x
b)
.27
c)
13
d)
3.51
16.
The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor?
a)
.08
b)
1.08
c)
.92
d)
8
17.
The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?
a)
9766
b)
9006
c)
9765
d)
5433
18.

Using the table below, find the equation that matches

a)

y = 20(2)x

b)

y = 20(1/2)x

c)

y = 2(20)x

d)

y = 20(1.25)x

19.

Great Amusements Park has been raising its ticket prices every year, as shown in the table. Write an equation that represents the ticket price for year x.

a)

y = 5x + 50

b)

y = 50(1.10)x

c)

y = 42.5(1.05)x

d)

y = 50(5)x

20.

Determine the population for year 3 of the table.

a)

8.2

b)

8.4

c)

8.64

d)

9

21.

Write an equation that presents the population for any year.

a)

y = x + 5

b)

y = 5(1)x

c)

y = 1.2x + 5

d)

y = 5(1.2)x

22.
Which of the equations below represent this table?
a)
y=3⋅(36)x
b)
y=36⋅(3)x
c)
y=3⋅(⅓)x
d)
y=36⋅(⅓)x
23.
The attendance at the art museum at the New Year’s opening was 250 people. The attendance has been increasing at a rate of 3% each month. How many people will attend by the end of a year?
a)
356
b)
265
c)
5825
d)
1329
24.
A car is purchased for $28,000.  The value of the car depreciates 15% per year.  What is the value of the car after 5 years?
a)
$12,424
b)
$10,560
c)
$5,600
d)
$56,318
25.

What is the asymptote of y = 2x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

26.

The asymptote of y = 2x + 4 will shift...

a)

up four to y = 4

b)

down four to y = -4

c)

not shift at all and remain y = 0

27.
Simplify
4-2
a)
1/16
b)
16
c)
1/4-2
d)
8
28.
Solve for x using the same base method.
3x-20 = 27
a)
17
b)
27
c)
-7
d)
23
29.
272x = 3x-7
a)
-7/3
b)
-1
c)
-5/7
d)
-7/5
30.
Solve: 2x = 4x+1
a)
-2
b)
2
c)
-3
d)
3
31.
Solve for a:
5a + 2 = 1/125
a)
-1
b)
-6/7
c)
-5
d)
4
32.
Solve: 7-x = 49
a)
x = 1
b)
x = -1
c)
x = 2
d)
x = -2
33.

Solve 33 = (32)2x + 1

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

34.
To solve 8 = 25x+7, you would need to re-write 8 as what base?
a)
8
b)
4
c)
2
d)
Cannot be determined
35.
Solve for x:
(-3)x = (-3)13
a)
13
b)
-3
c)
x + 13
d)
x -13
36.
In an exponential function, what does the 'a' represent? 
a)
SLOPE
b)
RATE OF CHANGE
c)
Y-INTERCEPT
d)
COMMON RATIO
37.
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? 
a)
0 people
b)
It doesn't say
c)
I don't know
d)
6191
38.
The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)t where t is the number of years since 1990. What percent did the population increase each year?
a)
4%
b)
It doesn't say
c)
I don't know
d)
400%
39.
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 the year 2011?
a)
$344,022
b)
$31,500
c)
$15,000
d)
$28,500
40.
During normal breathing, about 12% of the air in the lungs is replaced after one breath. Write an exponential decay model for the amount of the original air left in the lungs if the initial amount of air in the lungs is 500 mL. How much of the original air is present after 240 breaths?
a)
Just about zero mL
b)
60 mL
c)
440 mL
d)
0 mL
41.
An adult takes 400 mg of ibuprofen. Each hour, the amount of ibuprofen in the person’s system decreases by about 29%. How much ibuprofen is left after 6 hours? 
a)
51 mg
b)
284 mg
c)
1843 mg
d)
116 mg
42.
You buy a new computer for $2100. The computer decreases by 50% annually. When will the computer have a value of $600?
a)
between 1 and two years
b)
more than 5 years
c)
less than a year
d)
between 3 and 4 years
43.
You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system decreases by about 12%. How long until you have 10mg of caffeine? 
a)
19 to 20 hours
b)
10 to 20 hours
c)
15 to 16 hours
d)
5 to 6 hours
44.
The foundation of your house has about 1,200 termites. The termites grow at a rate of about 2.4% per day. How long until the number of termites doubles?
a)
29 to 30 years
b)
23 to 24years
c)
15 to 16 years
d)
19 to 20 years
45.
The population of Bloom Falls, Mass. (population 937) is slowly moving to a bigger city.
Every year the population drops by 4.5%. What is the population after 3 years?
a)
1,069 people
b)
894 people
c)
816 people
d)
854 people
46.

You bought a boat in 2004 for $12,500. The boat's value depreciates by 7% a year. How much is the boat worth in 2012?

a)

$11625

b)

$6994.77

c)

$21,477

d)

$875

47.
The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.
a)
y=1400(1.09)x
b)
y=1.09(1400)x
c)
y=1400(.91)x
d)
y=1.09x
48.
Adding 4 to the equation y=2(1.4)x would do what to the graph?
a)
Move it up 4
b)
Movie it down 4
c)
Move it right 4
d)
Move it left 4
49.
In 1985, there were 285 cell phone subscribers in the small town of Centerville. The number of subscribers increased by 75% per year after 1985. How many cell phone subscribers were in Centerville in 1994?
a)
OVERFLOW
b)
1994
c)
1000
d)
43871
50.
Each year the local country club sponsors a tennis tournament. Play starts with 256 participants. During each round, half of the players are eliminated. How many players remain after 5 rounds? 
a)
2
b)
4
c)
16
d)
8
51.
Isaac has $30 in a savings account. The interest rate is 5%, compounded annually.
To the nearest cent, how much will he have in 2 years?
a)
$33.08
b)
$3.08
c)
$31.50
d)
$1.50
52.
Is this exponential growth or decay?
y = 7(1.2)x
a)
Growth, because of 7
b)
Decay, because of 1.2
c)
Growth because of 1.2
d)
Decay because of 7
53.
Is this exponential growth or decay?
a)
Growth because a=1
b)
Decay because b=0.5
c)
Growth because there is no a
d)
Neither because a=0
54.
James' 70 in. giant peach doubles in size every week. Write an expression that would represent how big the peach is after 5 weeks.
a)
y = 70(2)35
b)
y = 70(2)5
c)
y = 2(70)5
d)
y = 5(70)2
55.
Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.
a)
y=6(0.14)x
b)
y=6(1 + 14)x
c)
y=6(1 + .14)x
d)
y=6(0.86)x
56.
The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)t where t is the number of years since 1990. What percent did the population increase each year?
a)
104%
b)
4%
c)
40%
d)
400%
57.
What is the starting amount for the following function:
f(x) = 3(1/3)x 
a)
0
b)
1/3
c)
1
d)
3
58.
Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.
a)
y=5000(0.7)x
b)
y=30(5000)x
c)
y=5000(1.3)x
d)
y=5000xx
59.

A biologist studying squirrels created a function to model their population growth from 1990, p(t) = 5(2)t where,t = is the number of years past 1990 and p(t) = population of squirrels. How many squirrels will there be in 1992?

a)

5 squirrels

b)

10 squirrels

c)

20 squirrels

d)

40 squirrels

60.
What is the horizontal asymptote?
a)
y = 2
b)
y = -2
c)
x = 2
d)
y = 0
61.
A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?
a)
14327
b)
4309
c)
839
d)
7680
62.
Which equation best describes the graph? 
a)
y = 2x + 4
b)
y = 2x - 3
c)
y = 2x - 4
d)
y = 2x + 3 
63.

How long ( in minutes) will it take for 150 students to hear the rumor?

a)

10.4

b)

624

c)

-1

d)

-60

64.

Middletown High School has student elections every year. Lately, the school has seen a 5% decrease in voting from election to election. If 910 students voted this year, how many will be expected to vote 8 years from now? (Round to the nearest whole number if necessary).

a)

604

b)

777

c)

29

d)

198

65.

More and more people are purchasing food from farmers' markets. As a consequence, a market researcher predicts that the number of farmers' markets will increase by 15% each year. If there are 6,200 farmers' markets this year, how many will there be in 10 years? (Round to the nearest whole number if necessary).

a)

25,082

b)

12,937

c)

62,000

d)

43,511

66.

Thanks to its environmental initiatives, Silvergrove has cut its annual CO2 emissions by 5%. This year, the town produced 290,000 metric tons of emissions. If the downward trend continues, how much CO2 will be produced 7 years from now? (Round to the nearest whole number if necessary).

a)

202,518

b)

135,792

c)

78,376

d)

20,658

67.

The mice population is 25,000 and is decreasing by 20% each year. What will be the mice population after 3 years?

a)

12,800

b)

15,777

c)

102, 475

d)

2,500

68.

The number of tadpoles in the pond triples each day.


Which graph best represents the relationship between time and the number of tadpoles?

a)
b)
69.

Bao has an original oil painting worth 30,000 Chinese Yuan. Each year the painting's value increases by 15%.


Which graph best represents the relationship between time and the painting's value?

a)
b)
70.

You work as a taxi driver. You earn an average of $75 in tips every day.


Which graph best represents the relationship between time and the cumulative total of your tips?

a)
b)
71.

Which function is represented by the table?

a)

y = x + 2

b)

y = 3x2

c)

y = 3x

d)

y = 2(3)x

72.

The table shows the temperature, t(m), of a cup of hot chocolate that is allowed to chill over several minutes, m.

Which expression best fits the data for T(m).

a)

150(0.85)x

b)

150(1.15)x

c)

150(0.85)x-1

d)

150(1.15)x-1

73.

What is the equation for this graph?

a)

y=3(2)x

b)

y=2(3)x

c)

y=4(2)x

d)

y=2(5)x

74.

What is the equation for this graph?

a)

y=2x - 3

b)

y=2x - 2

c)

y=2x - 4

d)

y=3x - 3

75.
Is the graph exponential growth or decay?
a)
Exponential growth
b)
Exponential decay
76.
Given y=3x determine the y-intercept 
a)
(0,1)
b)
(0,3)
77.

What is the asymptote of the parent function y=2x?

a)

x=0

b)

y=0

c)

x=2

d)

y=2

78.
What is the y-intercept?
a)
(0,0)
b)
(0,1)
c)
(-3,0)
d)
(0,-3)
79.
What is the asymptote value in the function?
a)
3
b)
2
c)
7
d)
0
80.

You are sick and your doctor prescribes a medication. One dose is 200 mg. Every half hour 30% of the medication leaves the body. If you take the first dose at 6 am, how many events/intervals have occurred by 9 am?

a)

3

b)

6

c)

30

d)

90

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