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Exponential vs. Constant Growth & Decay - Printable Mathematics Worksheets - Wayground

Exponential vs. Constant Growth & Decay

20 questions

8th - 8th Grade

Mathematics

Designed for Grade 8 mathematics, Exponential vs. Constant Growth & Decay gives students 20 multiple-choice questions on distinguishing exponential growth, exponential decay, and linear functions. Students interpret equations and graphs, identify growth or decay rates from exponential expressions, select models for real-world situations, and determine appropriate equations for repeated change. Contexts include population changes, museum attendance, turtle populations, compound interest, and annual investment returns. This free printable worksheet with an answer key helps students connect the multiplier in an exponential model to the percent rate and the number of time periods. It also provides practice translating verbal descriptions into exponential equations and evaluating those models to solve applied problems. Use it for Grade 8 algebra practice, guided instruction, independent review, or a quick formative assessment of whether students can recognize and apply exponential patterns rather than treating all change as linear.

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Exponential vs. Constant Growth & Decay

Total questions: 20

Name
Class
Date
1.
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
2.
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
3.
Is the pictured graph growth, decay, or linear or none?  
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None
4.
Give the rate of decay:
y = 35(0.65)x
a)
35%
b)
65%
c)
.35%
d)
165%
5.
Give the rate of growth:
y = 5(1.27)x
a)
127%
b)
27%
c)
5
6.
The population of turtles is doubling every 3 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)8
d)
y = 400 + 2(8)
7.
Is this exponential growth or decay?
a)
Growth, because of 7
b)
Decay, because of 1.2
c)
Growth because of 1.2
d)
Decay because of 7
8.
Pick the equation that is exponential growth
a)
y=2(0.5)x
b)
y = 0.5(2)x
c)
y = .5x - 2
d)
y = 2x + .5 
9.
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
10.
Your 2 year investment of $5,300 earns 2.9% and is compounded annually.  What will your total return be?
a)
$5,304.46
b)
$5,611.86
c)
$5,613.28
d)
$8,819.73
11.
A city has a population of 21,517 based on a census taken in 1998. If the population is expected to grow by 11% annually, what will the population be in the year 2030?
a)
606,900
b)
517
c)
492,573
d)
None of these
12.
What type of function is this equation:
y=  4x+1
a)
Linear
b)
Exponential
c)
Neither
13.
What type of function describes the story below?
You have $5 and triple your money every day. 
a)
Linear
b)
Exponential
c)
Neither
14.
Is the pictured graph exponential growth, exponential decay, linear growth, or none?  
a)
Exponential Growth
b)
Exponential Decay
c)
Linear Growth
d)
None of the above
15.
What function type models this graph?
a)
Exponential Growth
b)
Exponential Decay
c)
Linear Growth
d)
Quadratic
16.
Twenty years ago, Mr. Stern 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
17.
Write an equation that models the following situation:
Caroline'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
18.
What type of function is this equation:
y= -3x + 12
a)
Constant Growth
b)
Exponential Growth
c)
Exponential Decay
d)
Constant Decrease
19.
Connor bought a brand new Ford F-150 for $45,000.  Unfortunately, the value of the truck depreciates at a rate of 1.3% per month.  Which equation shows the value of the truck?
a)
45,000(1.3)x
b)
45,000(1.013)x
c)
45,000(.987)x
d)
45,000(.013)x
20.
Connor bought a brand new Ford F-150 for $45,000.  Unfortunately, the value of the truck depreciates at a rate of 1.3% per month.  Use your equation to find the value of the truck after 5 years.
a)
$42,150.07
b)
$20,523.03
c)
$.17
d)
$22,428.94
Answer Key

Exponential vs. Constant Growth & Decay

Total questions: 20

1.
a) 356
2.
c) 816 people
3.
b) Exponential Decay
4.
a) 35%
5.
b) 27%
6.
c) y = 400(2)8
7.
c) Growth because of 1.2
8.
b) y = 0.5(2)x
9.
b) y = 15(1.35)x
10.
b) $5,611.86
11.
a) 606,900
12.
b) Exponential
13.
b) Exponential
14.
a) Exponential Growth
15.
a) Exponential Growth
16.
b) $424,527.63
17.
c) y=6(1.14)x
18.
d) Constant Decrease
19.
c) 45,000(.987)x
20.
b) $20,523.03

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FAQs

What does the Exponential vs. Constant Growth & Decay worksheet cover?

This Grade 8 mathematics worksheet uses 20 multiple-choice questions to build skill in distinguishing exponential growth, exponential decay, and linear functions. Students interpret graphs and equations, identify rates such as the 35% decay represented by a 0.65 multiplier, choose exponential models, and solve population, attendance, turtle, and compound-interest problems.

How can I use this worksheet to teach exponential growth and decay?

Introduce the worksheet by having students compare a constant additive change with a repeated multiplicative change, then model how a multiplier above 1 indicates growth and a multiplier between 0 and 1 indicates decay. Work through an equation-identification or graph item together before students apply the same reasoning to the population, investment, and repeated-growth scenarios in the multiple-choice set.

What mistakes should I watch for when students complete this worksheet?

Students may report the multiplier as the percent rate—for example, choosing 65% instead of the 35% decay represented by 0.65—or use 35 rather than 1.35 for a 35% growth model. Also check that they count time intervals correctly, distinguish exponential equations from linear equations, and identify the base rather than the initial amount when deciding whether a model represents growth or decay.

How do I assign and grade this worksheet?

The Exponential vs. Constant Growth & Decay worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. You can grade printable submissions by scanning student work with the Wayground for Teachers app, while the digital quiz supports online completion and grading.

How can I differentiate this exponential growth and decay worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the equations, graph questions, and answer choices are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when those options better support students working with the exponential models and word problems.

Where can I find more free worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more worksheets at https://wayground.com/en-us/worksheets.

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