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Unit 9, Lesson 21

Predicting Populations

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Integrated Math 1

Practice

Problem 1

ForLesson 11: Modeling Exponential Behavior

The table shows the height of a ball after different numbers of bounces.

$n$	1	2	3	4	5
$h$	83	61	46	35	26

Can the height, $h$, in centimeters, after $n$ bounces be modeled accurately by a linear function? Explain your reasoning.
Can the height, $h$, after $n$ bounces be modeled accurately by an exponential function? Explain your reasoning.
Create a model for the height of the ball after $n$ bounces, and plot the predicted values with the data.
Use your model to estimate the height the ball was dropped from.
Use your model to estimate how many bounces it takes before the rebound height is less than 10 cm.

Mai used a computer simulation to roll number cubes and count how many rolls it took before all of the cubes came up sixes. Here is a table showing her results.

*$d$,* number of cubes	1	2	3	4
*$r$,* number of rolls	5	31	143	788

Would a linear or exponential function be appropriate for modeling the relationship between $d$ and $r$? Explain how you know.

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Predicting Populations

Practice

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

*\(d\),* number of cubes	1	2	3	4
*\(r\),* number of rolls	5	31	143	788

\(n\)	1	2	3	4	5
\(h\)	83	61	46	35	26