WorksheetsExponential Growth and Decay
Total questions: 80
Worksheet time: 7hrs 40mins
Name
Class
Date
1.
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
2.
Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?
a)
$23,219.72
b)
$136.72
c)
$51,710.94
d)
$16,710.94
3.
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
4.
Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?
a)
$176,783.29
b)
$424,527.63
c)
$57,357.75
d)
$532,041,076.80
5.
Is this exponential growth or decay?
a)
Growth
b)
Decay
6.
What is the initial value for the function: f(x) = 300(1.16)x?
a)
300
b)
1.16
c)
.16
d)
x
7.
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
8.
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
9.
What is b, the common ratio, for the function: f(x) = 300(1.16)x?
a)
300
b)
1.16
c)
.16
d)
x
10.
Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)6
A=1200(.85)6
a)
Growth
b)
Decay
11.
Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)3
A=10(1.01)3
a)
Growth
b)
Decay
12.
What type of function is y = 7(5/4)x?
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None of the above
13.
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
14.
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)
70(2)35
b)
70(2)5
c)
2(70)5
d)
5(70)2
15.
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.
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
16.
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
17.
Suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%. If no other money is added or withdrawn from the account, how much will be in the account after 10 years?
a)
$3122.18
b)
$4994.50
c)
$4440.73
d)
$86,776.40
18.
If you have $10, and your money doubles every year, how much money will you have in 10 years?
a)
$50
b)
$100
c)
$5120
d)
$10240
19.
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
20.
A population of 1500 deer decreases by 1.5% per year. At the end of 10 years, there will be approximately 1290 deer in the population. Which function can be used to determine the number of deer, y, in this population at the end of t years?
a)
y = 1500(1 - 0.015)t
b)
y = 1500(0.015)t
c)
y = 1500(1 + 0.015)t
d)
y = 1500(1.5)t
21.
There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 3.75% per month. At this rate of growth, which function can be used to determine the monthly cell phone sales x months after January?
a)
f(x) = 417(3.75)x
b)
f(x) = 417(0.0375)x
c)
f(x) = 417(1.0375)x
d)
f(x) = 417(1.375)x
22.
a)
The graph represents an exponential growth situation.
b)
Eventually, the car will be worth exactly $0.
c)
The starting value of the car was $12,000.
d)
The range for the situation is y ≥ 0.
23.
a)
x > 0
b)
y > 0
c)
-∞ < x < ∞
d)
-∞ < y < ∞
24.
An antibiotic is introduced into a colony of 12,000 bacteria during a laboratory experiment. The colony is decreasing by 14.9% per minute. Which function can be used to model the number of bacteria in the colony after x minutes?
a)
f(x) = 12000(1 + 14.9)x
b)
f(x) = 12000(1 - 14.9)x
c)
f(x) = 12000(1 + 0.149)x
d)
f(x) = 12000(1 - 0.149)x
25.
Some banks charge a fee for a savings account that is left inactive for an extended period of time. The equation y = 5000(0.98)x represents the amount remaining, y, of one account that was left inactive for a period of x years. What does the number 5000 represent in this situation?
a)
A fee charged for an inactive account
b)
The percent of money in the account after x years
c)
The amount of money in the account initially
d)
The amount of money in the account after x years
26.
a)
f(x) = 35(0.95)x
b)
f(x) = 36(0.05)x
c)
f(x) = 35(1.05)x
d)
f(x) = 36(1.5)x
27.
A child asks her dad for an allowance that starts with a penny and then doubles every day for a month. Which function can be used to model the amount of money, A, the child will receive each day, x?
a)
A(x) = 2(0.01)x
b)
A(x) = 0.01(2)x
c)
A(x) = 0.01(1 - 2)x
d)
A(x) = 2(1.01)x
28.
a)
F
b)
G
c)
H
d)
J
29.
a)
The graph of this situation represents exponential decay.
b)
The range of this function is y > 0.
c)
There is a horizontal asymptote at y = 0 for this situation.
d)
The y-intercept is (0, 230).
30.
a)
-∞ < y < ∞
b)
y > 0
c)
-∞ < x < ∞
d)
x > 0
31.
a)
The number of players decreases by 30% each round.
b)
The range for the function is 1 < y < 5.
c)
The domain for the function is 5 < x < 65.
d)
The situation represented is exponential decay.
32.
a)
F
b)
G
c)
H
d)
J
33.
The function to find the value of a car after t years is given by v(t) = 24,000(.75)t Which of the following statements is not true?
a)
The starting value of the car was $24,000.
b)
The y-values of the graph increase as the x-values increase.
c)
The value of b indicates this is an exponential decay situation.
d)
The horizontal asymptote is y = 0, which means the car will never have a value of $0.
34.
What is a, the starting term, for the function: f(x) = 300(1.16)x?
a)
300
b)
1.16
c)
.16
d)
x
35.
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 + 0.35)x
c)
y = 15(0.35)x
d)
y = 35(1+ 0.15)x
36.
Is the pictured graph growth, decay, or linear or none?
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None
37.
Is this exponential growth or decay?
a)
Growth
b)
Decay
38.
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+ 0.14)x
d)
y=6(1 - 0.14)x
39.
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(1 - 0.30)x
b)
y=30(5000)x
c)
y=5000(1 + 0.30)x
d)
y=5000xx
40.
Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?
a)
$23,219.72
b)
$136.72
c)
$51,710.94
d)
$16,710.94
41.
Change 6.75% to a decimal.
a)
67.5
b)
.675
c)
675
d)
.0675
42.
The initial deposit or investment is called
a)
Interest
b)
Principal
c)
Savings
d)
Capital gain
43.
Semi-Annually means how many times a year?
a)
4
b)
2
c)
1
d)
6
44.
Monthly means how many times a year?
a)
4
b)
12
c)
52
d)
365
45.
Change 11.2% to a decimal.
a)
11.2
b)
1.12
c)
0.112
d)
0.0112
46.
Bruno was given $2000 when he turned 3 years old. His parents invested it at a 2% interest rate compounded annually. No deposits or withdrawls were made. Which expression can be used to determine how much money Bruno had in the account when he turned 16?
a)
2000(1+0.02)13
b)
2000(1-0.02)13
c)
2000(1+0.02)16
d)
2000(1-0.02)16
47.
A stamp gets more expensive each year. It increases in value by 60 % each year. What is the growth FACTOR?
a)
.6
b)
1.06
c)
1.6
d)
.4
48.
Suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%. What is the growth factor?
a)
.96
b)
1.4
c)
1.04
d)
$3000
49.
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
50.
Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?
a)
$23,219.72
b)
$136.72
c)
$51,710.94
d)
$16,710.94
51.
Since January 1980, the population of the city of Brownville has grown according to the mathematical model y=720,500(1.022)x, where x is the number of years since January 1980. What is the was the population of Brownville in 1980?
a)
102.2 people
b)
720,500 people
c)
1.022 people
d)
1022 people
52.
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
53.
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
54.
You buy a new computer for $2100. The computer decreases by 50% annually. How much is it worth after 2 years.
a)
225
b)
325
c)
425
d)
525
55.
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?
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
56.
The city of Whoville has been much more stable since the Grinch turned his life around. The population of 900 is increasing at a rate of 7.5% per year. If the population continues growing at the same rate, how many people will there be in 11 years?
a)
424288
b)
1994
c)
10642
d)
900
57.
The Country of Puerto has 3,370,000 people in it and is decreasing at a rate of 4.5%. Estimate the population after 40 years.
a)
534,275
b)
19,601,148
c)
1,350,756
d)
2,521,541
58.
Pick the equation that is exponential growth
a)
y=2(0.5)x
b)
y = 0.5(2)x
59.
Pick the equation that is exponential decay
a)
y=2000(0.88)
b)
y=0.5(1.88)
60.
Since January 1980, the population of the city of Brownville has grown according to the mathematical model y=720,500(1.022)x, where x is the number of years since January 1980. What is the percentage increase of the population annually?
a)
720,500%
b)
102.2%
c)
2.2%
d)
22%
61.
The half-life of Zn-71 is 2.4 minutes. If one had 100.0 g at the beginning, how many grams would be left after 7.2 minutes has elapsed?
a)
100.0g
b)
50.0g
c)
12.5g
d)
8.5g
62.
The half-life of strontium-90 is 25 years. How much strontium-90 will remain after 100 years if the initial amount is 4.0 g?
a)
3.0g
b)
0.25mg
c)
0.3g
d)
0.25g
63.
Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.
a)
$15,415.94
b)
$15,683.28
c)
$15,927.56
d)
$16,109.05
64.
Give the rate of decay:
y = 35(0.65)x
y = 35(0.65)x
a)
35%
b)
65%
c)
.35%
d)
165%
65.
Give the rate of growth:
y = 5(1.27)x
y = 5(1.27)x
a)
127%
b)
27%
c)
5
66.
Describe the function:
y = 57(1/3)x
y = 57(1/3)x
a)
growth by factor of 1/3
b)
decay by factor of 1/3
c)
growth by 2/3
d)
decay by 1/3 %
67.
Describe the function:
y = 1000(1 - 0.87)x
y = 1000(1 - 0.87)x
a)
growth by 87%
b)
decay by 87%
c)
growth by 13%
d)
decay by 13%
68.
Is the pictured graph growth, decay, or linear or none?
a)
Growth
b)
Decay
c)
Linear
d)
None
69.
Is the equation linear, exponential or neither?
a)
Linear
b)
Exponential
c)
Neither
70.
What type of function is y = 7(5/4)x?
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None of the above
71.
Give the value of the growth factor:
y = 35(1.075)x
y = 35(1.075)x
a)
35
b)
0.075
c)
7.5%
d)
1.075
72.
Determine the y-intercept of the function:
y = 1.25(5)x
y = 1.25(5)x
a)
5
b)
1
c)
.25
d)
1.25
73.
The population of turtles is doubling every 6 months. If there are 400 turtles now, how many will there be in 2 years? (Choose equation)
a)
y = 400(2)2
b)
y = 400(2)6
c)
y = 400(2)4
d)
y = 400 + 2(8)
74.
Give the rate of growth:
y = 35(1.075)x
a)
7.5%
b)
0.075 %
c)
75%
d)
.75%
75.
In an exponential function, what does the 'a' represent?
a)
SLOPE
b)
RATE OF CHANGE
c)
Y-INTERCEPT
d)
COMMON RATIO
76.
Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased by 5% per year. How much is the home worth today?
a)
$176,783.29
b)
$424,527.63
c)
$57,357.75
d)
$532,041,076.80
77.
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
78.
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.
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
79.
A population of fish starts at 8,000 and decreases by 6% per year. What formula models this situation?
a)
P = 8000(0.6)x
b)
P = 8000(1.6)x
c)
P = 8000(1.06)x
d)
P = 8000(0.94)x
80.
100*3*3*3*3 written in exponential form is
a)
34
b)
1004
c)
3(1004)
d)
100(34)
100 %
