## Reflection: Developing a Conceptual Understanding Comparing Linear and Exponential Functions Day 1 - Section 2: Investigation

This is a problem that all students can access.  When students were sharing what they found, I started with a group that had started to make a list for each payment option but had not found the place where the second option became better than the first.  After this group, I let another group show their work and they had found that after 12 bags of leaves, the second option would be better.  They showed this using a list of values organized into a table.  A third group showed something similar but also pointed out that the first payment option was going up by \$2 each time while the second was doubling each time.  They showed how this would lead to a really good payday for bags 12, 13, 14, etc.  I also had a group show the equation y=2x for the linear model and the equation y=.02(2)^x for the exponential model.  I asked the group what their exponential model would give as an output on the first day...As soon as they saw it was 4 cents rather than two, they realized they would have to adjust their model to y=0.01(2)^x.

Comparing Growth Rates
Developing a Conceptual Understanding: Comparing Growth Rates

# Comparing Linear and Exponential Functions Day 1

Unit 7: Exponential Functions
Lesson 11 of 13

## Big Idea: Exponential and linear growth appear similar at first but exponential growth will eventually outpace linear growth.

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Standards:
Subject(s):
Math, Algebra, exponential growth, linear models, exponential function, linear functions, Function Operations and Inverses, rate of change, function, ratio, geometric patterns, exponential decay
40 minutes

### James Bialasik

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