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Exponential Models -Extra Practice

Total questions: 60

Worksheet time: 2hrs 59mins

Name
Class
Date
1.
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
2.
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
3.
Identify the y-intercept (initial value) in the function f(x)=13(.27)x
a)
(.27)x
b)
.27
c)
13
d)
3.51
4.
Identify the common ratio (multiplier) of the function f(x)=2(4)x.
a)
2
b)
4
c)
(2)x
d)
8
5.
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
6.
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
7.

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

8.
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
9.

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

10.
What is a, the starting term, for the function: f(x) = 300(1.16)x?
a)
300
b)
1.16
c)
.16
d)
x
11.
Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)6
a)
Growth
b)
Decay
12.
Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)3
a)
Growth
b)
Decay
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.
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
15.

What is the domain of the function shown?

a)

All real numbers

b)

y>0y>0  

c)

All real numbers greater than 1

d)

y<0y<0  

16.

What is the range of the function shown?

a)

All real numbers

b)

y>0y>0  

c)

All real numbers greater than 1

d)

y<0y<0  

17.
What is the y-intercept of the function?
a)
2
b)
3
c)
1
d)
-2
18.
Is the pictured graph growth, decay, or linear or none?  
a)
Exponential Growth
b)
Exponential Decay
19.

Is the following function and example of decay or growth?

f(x)=2(0.85)x

a)

Exponential Decay

b)

Exponential Growth

20.
What type of function is y = 7(5/4)x?
a)
Exponential Growth
b)
Exponential Decay
21.

Which represents exponential decay?

a)

A

b)

B

c)

C

d)

D

22.
The expression 12(1.015)t models the population of elephants in a wildlife refuge after t years since 1975.
Is the population of elephants increasing or decreasing?
a)
Increasing
b)
Decreasing
23.

In an exponential function, what does the 'a' represent?

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

24.
Identify the y-intercept (initial value) in the function f(x)=13(.27)x
a)
(.27)x
b)
.27
c)
13
d)
3.51
25.
Is the pictured graph growth, decay, or linear or none?  
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None
26.
What type of function is f(x)=2(1/7)x ?
a)
Exponential Growth
b)
Linear
c)
Exponential Decay
d)
None of the Abovee
27.
What is the x-intercept of the exponential function? 
a)
(0,1)
b)
(0,0)
c)
There is not one
28.

Which function models this table?

a)

f(x)=2⋅4xf\left(x\right)=2\cdot4^x

b)

f(x)=4xf\left(x\right)=4^x

c)

f(x)=4⋅2xf\left(x\right)=4\cdot2^x

d)

f(x)=8xf\left(x\right)=8^x

29.

What is the equation of the horizontal asymptote for following exponential function?

a)

y = -4

b)

y > -4

c)

y < -4

d)

(0, -3)

30.

What is the equation of the horizontal asymptote for following exponential function?

a)

y = -2

b)

y > -2

c)

y < -2

d)

(0, -2)

31.

What is the equation of the horizontal asymptote for following exponential function?

a)

y = 1

b)

y = 2

c)

y > 1

d)

(0, 2)

32.
Given y=3x determine the asymptote
a)
(0,1)
b)
(0,3)
c)
x=0
d)
y=0
33.
What is the range of f(x) = 5x?
a)
-∞ ≤ x ≤ ∞
b)
-∞ ≤ y ≤ ∞
c)
x > 0
d)
y > 0
34.

What is the Range of this function?

a)

y> 0

b)

x> 0

c)

All Real Numbers

d)

y= 1

35.

What is the range of the exponential function?

a)

all real numbers

b)

y > -1

c)

y < -1

d)

x > -1

36.

What is the range of the exponential function?

a)

all real numbers

b)

y > 3

c)

y < 3

d)

x > 3

37.

What is the range of the exponential function?

a)

all real numbers

b)

y > -3

c)

y < -3

d)

x > -3

38.
What is the range of this graph?
a)
y = 6
b)
(0, -4)
c)
y > -6
d)
y < -6
39.

What is the horizontal asymptote of this function?

a)

x=3x=3  

b)

x=−3x=-3  

c)

y=3y=3  

d)

y=−3y=-3  

40.

What is the range of this function?

a)

y<5y<5

b)

y<−5y<-5

c)

y≤5y\le5

d)

y≤−5y\le-5

41.

What is the equation of the horizontal asymptote for following exponential function?

a)

y = -4

b)

y > -4

c)

y < -4

d)

(0, -3)

42.

Which of the following is an exponential function?

a)

y = x2

b)

f(x) = 3x3

c)

y = x3

d)

f(x) = 3x

43.
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
44.
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
45.
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
46.

The amount of ants in a colony, f, that is decaying can be modeled by

f(x) = 800(.87)x, where x is the number of days since the decay started.

Suppose f(20) = 49. Which of the following is true?

a)

After 20 days, there are 49 ants in the colony.

b)

After 49 days there are 20 ants in the colony.

c)

The amount of ants times 20 is 49.

d)

After 20 days the amount of ants remaining decreases by 49.

47.
The expression 12(1.015)t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 1.015 represent?
a)
The number of elephants was 1,015 in 1975.
b)
The number of elephants increases by 1.5% each year.
c)
The number of elephants increases by 101.5% each year.
d)
The number of elephants is multiplied by 1.015 each year.
48.
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
49.

What game are these people playing?

a)

Twister

b)

Connect 4

c)

Spin & Kick

d)

Sorry

50.

Who is this wizard?

a)

Hermione Granger

b)

Ron Weasly

c)

Harry Potter

d)

Draco Malfoy

51.

What is this characters name?

a)

Luigi

b)

Mario

c)

Zelda

d)

Link

52.

What social media app does this picture belong to?

a)

Instagram

b)

Facebook

c)

Snapchat

d)

Snapbook

53.

What was the first Disney World park?

a)

Animal Kingdom

b)

Epcot

c)

Magic Kingdom

d)

Hollywood Studios

54.

Who is the fashion designer in The Incredibles?

a)

Edna Mow

b)

Edna Mode

c)

Violet

d)

Dash

55.

Mary’s father has 5 daughters – Nana, Nene, Nini, Nono. What is the fifth daughter's name?

a)

Nunu

b)

Dazlyn

c)

Mary

d)

Janet

56.

What movie is this?

a)

The Lion, The Witch, and The Wardrobe

b)

The Lion King

c)

Life of Pi

57.
a)

Snow Queen

b)

Frozen

c)

Happy Feet

58.
a)

It

b)

Red Ballon

c)

Stranger Things

59.
a)

Moana

b)

Sharktales

c)

Spogebob

60.
a)

Sherlock Holmes

b)

The Little Mermaid

c)

Finding Nemo

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