Unit 5
Modeling Exponential Behavior
Intro to Exponential Functions
Lesson 11
HSF-LE.A: Construct and compare linear, quadratic, and exponential models and solve problems.
HSF-LE.B.5: Interpret the parameters in a linear or exponential function in terms of a context.
HSN-Q.A.1: Reason quantitatively and use units to solve problems.
HSN-Q.A.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
HSF-IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
HSF-IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables.
HSF-IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
HSS-ID.B.6.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
HSF-BF.A.1: Write a function that describes a relationship between two quantities..
Expressions and Equations
Wondering about Windows
Unit 5 ● Lesson 11
Domain: 0 < x < 44
Range: 0 < y < 1,100
Domain: 0 < x < 10
Range: 0 < y < 450
Domain: -10 < x < 80
Range: 10 < y < 100
Warm-up
Page 254
Page 361
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 5 ● Lesson 11
Let’s use exponential functions to model real life situations.
We can determine an appropriate model for the situation described by the data so that we can use exponential functions to model situations that involve exponential growth or decay.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Where were we? Where are we? Where are we going?
Unit 5 ● Lesson 11
Agenda Review
You are successful today when...,
● You can use exponential functions to model situations that involve exponential growth or decay.
● When given data, you can determine an appropriate model for the situation described by the data.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.2 Activity: Beholding Bounces
I can use exponential functions to model situations that involve exponential growth or decay.
10 mins Total
7 mins group - 3 mins class share
pg 362
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.2 Activity: Beholding Bounces
I can use exponential functions to model situations that involve exponential growth or decay.
10 mins Total
7 mins group - 3 mins class share
pg 354-5
Exponential. An exponential function of the number of bounces would decrease by the same factor for each successive bounce. It looks like each successive bounce is about half as high as the previous bounce, making an exponential model appropriate.
Plotting the points in the plane, they are not close to being on a line. A linear function of the number of bounces would decrease by the same amount for each successive bounce. The differences in heights between successive bounces are not close to being the same.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.2 Activity: Beholding Bounces
I can use exponential functions to model situations that involve exponential growth or decay.
Yes. The first rebound is a little over 53%, the second is almost 54%, and the fourth is 55%. The third rebound is only about 47% but there could be some measurement error.
or No, the third rebound is less than 50% of the height from which the tennis ball fell, falling out of the allowable range.
or It is not possible to tell. One of the values is too low and the others are close enough to 53% that it is impossible to be sure whether the bounces of this ball fall within the regulations.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.2 Activity: Beholding Bounces
I can use exponential functions to model situations that involve exponential growth or decay.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
11.4 Activity: Beholding More Bounces
I can use exponential functions to model situations that involve exponential growth or decay.
10 mins Total
4 mins individual - 3 mins group - 3 mins class share
pg 364-5
More bouncy. Each bounce of this ball reaches a height that is about 0.7 times that of the previous bounce (vs. only 0.5).
Graph B is more appropriate. Only whole-number values make sense in this context.
No, the height of this ball after any given bounce will not be lower than that of the tennis ball because they were dropped from the same height and this ball has a greater rebound factor.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Modeling Exponential Behavior
I can use exponential functions to model situations that involve exponential growth or decay.
Depending on the tools used, it can be very hard to get exact measurements of rebound heights, and it gets harder the lower the bounces are. Measurement errors are likely.
We might want to see if the differences are small enough to treat them as measurement error. In the lesson, they are all within about 0.05 of 0.5, and most of them are close to about 0.54.
We might disregard the factor(s) that are very different from the rest, or consider finding an average of the factors.
Lesson Synthesis
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Drop Height
I can use exponential functions to model situations that involve exponential growth or decay.
Between 150 cm & 180 cm.
The rebound factors are ⅕, ⅙, & 0. Because ⅕ of 150 is 30 & ⅙ of 180 is 30.
The ball was probably dropped from between 150 cm and 180 cm.
8
Cool-down
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Unit 5 ● Lesson 11
● I can use exponential functions to model situations that involve exponential growth or decay.
● When given data, I can determine an appropriate model for the situation described by the data.
Learning
Targets
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Glossary
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.
Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.