Curriculum  /  Math  /  9th Grade  /  Unit 6: Exponents and Exponential Functions  /  Lesson 20

Exponents and Exponential Functions

Lesson 20

Math

Unit 6

9th Grade

Lesson 20 of 22

Objective

Write, graph, and evaluate exponential decay functions.

Common Core Standards

Core Standards

  • F.BF.B.3 — Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
  • F.IF.C.7.E — Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
  • F.IF.C.8.B — Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01 12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
  • F.LE.A.1.C — Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Foundational Standards

  • 8.F.B.4

Criteria for Success

  1. Understand that an exponential decay function has a decreasing rate of change, represented by a value between $$0$$ and $$1$$, compared to an exponential growth function that has an increasing rate of change.
  2. Identify exponential decay functions in equations, tables, and graphs.
  3. Analyze an exponential decay function in equation form to identify features in the graph of the function including the $$y$$-intercept, domain, range, rate of change, etc.
  4. Analyze the graph of an exponential decay function to write an equation for the function.
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Anchor Problems

25-30 minutes

Problem 1

Compare and contrast functions $${{f(x)}}$$ and $${{g(x)}}$$ by answering the questions below. 

$${{f(x)}}=\left({1\over2}\right)^x$$

$${{g(x)}}=(2)^x$$

a.   What happens to the values of $${{f(x)}}$$ and $${{g(x)}}$$ as $$x$$ increases? 

b.   What are the domains of $${{f(x)}}$$ and $${{g(x)}}$$?

c.   What are the ranges of $${{f(x)}}$$ and $${{g(x)}}$$?

d.   Create a table of values for each function and use them to sketch a graph of each function.

Guiding Questions

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Problem 2

Consider the exponential graph below.

  1. Create a table of values for the function.
  2. Does the function represent exponential growth or exponential decay? Explain your reasoning. 
  3. What transformations were applied to the graph of this function? Explain your reasoning. 
  4. Determine the equation for this function.

Guiding Questions

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Problem 3

Sketch a graph of each function shown below.

$${f(x)=2(3)^{-x}}$$

$${g(x)=\left(1\over2\right)^x-3}$$

Guiding Questions

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Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

Problem 1

Graph the exponential function $${f(x)=-\left({1\over2}\right)^x}$$.

Problem 2

Write the equation for the graph shown below.

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems where students graph exponential decay functions, including those with transformations

Next

Identify features of exponential decay in real-world problems.

Lesson 21
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Exponent Rules, Expressions, and Radicals

Topic B: Arithmetic and Geometric Sequences

Topic C: Exponential Growth and Decay

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