Compare rates of change in linear and exponential functions shown as equations, graphs, and situations.
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This lesson focuses on understanding and making connections across situations, graphs, and equations of linear and exponential functions. Students are not asked to generate equations, graphs, or contexts; they will work on those skills and concepts in the lessons that follow.
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Complete "Avi and Benita's Repair Shop" by Desmos.
Avi and Benita's Repair Shop by Desmos is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed May 17, 2018, 12:43 p.m..
Two equations are shown below.
A: $${y=0.01(2^x)}$$
B: $${y=100x}$$
Two equations and their graphs are shown.
Equation 1: $${y=5x}$$
Equation 2: $${y=0.5(2^x)}$$
a) Label each graph with the appropriate equation.
b) Describe the change in $$y$$ in each function as $$x$$ increases by $$1$$.
c) Describe the behavior of the exponential graph over time, as compared to the linear graph.
d) Over approximately what interval is the linear function greater than the exponential function?
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Use the function shown below to answer the questions that follow.
a. Which equation matches the graph?
i. $${y=3(2^x )}$$
ii. $${y=2(3^x )}$$
iii. $${y=4x+2}$$
iv. $${y=2x+4}$$
b. Explain why you chose that equation in part (a).
c. What is the rate of change of this function?
d. Suppose the graph of $${y=150x}$$ was added to the graph above. Which function is greater over the domain interval $${1<x<5}$$? Will this function always be greater over all values of the domain? Explain your reasoning.