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Exponential Growth and Decay Worksheet

Grade 12 Math worksheet covering exponential growth and decay functions, including applications to real-world scenarios.

Grade 12 Math AlgebraExponential Growth and Decay
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Includes

Multiple ChoiceFill in the Blanks2 Short AnswerTrue / FalseGraph

Standards

CCSS.MATH.CONTENT.HSF.LE.A.1CCSS.MATH.CONTENT.HSF.LE.A.2CCSS.MATH.CONTENT.HSF.LE.B.5

Topics

AlgebraExponential FunctionsGrowthDecayGrade 12
8 sections · Free to use · Printable
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Exponential Growth and Decay

Name:

Date:

Score:

Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. Which of the following functions represents exponential decay?

a

y = 3(1.05)^x

b

y = 0.5(2)^x

c

y = 10(0.8)^x

d

y = 2x + 5

2. The initial population of bacteria in a petri dish is 500. If the population doubles every hour, which equation models the population P after t hours?

a

P = 500 + 2t

b

P = 500(2)^t

c

P = 2(500)^t

d

P = 500t^2

3. In the exponential function y = a(b)^x, 'a' represents the  , and 'b' represents the  .

4. If a quantity decreases by a constant percentage over time, it is undergoing exponential  .

5. A car depreciates at a rate of 15% per year. If the purchase price was $25,000, write an exponential function to model the car's value after t years.

6. A new strain of bacteria grows according to the function P(t) = 100e^(0.2t), where P is the population and t is in hours. What is the initial population and the continuous growth rate?

7. The graph of an exponential growth function always increases from left to right.

T

True

F

False

8. The base 'b' in an exponential decay function must be greater than 1.

T

True

F

False

9. A radioactive substance has a half-life of 10 years. If you start with 200 grams of the substance, how much will be left after 30 years? Show your calculations.

10. Sketch the graph of the function y = 2^x on the coordinate plane below.

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