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9-12 Algebra 2 Unit 5 Lesson 2

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K-5 Math 6-8 Math •9-12 Math

Course

Algebra 1 Geometry •Algebra 2 Extra Support Materials for Algebra 1

Unit

Unit 1 Unit 2 Unit 3 Unit 4 •Unit 5 Unit 6 Unit 7 Unit 8

Modeling Prompts

Lesson

Lesson 1 •Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18

K-5
6-8
9-12

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
Integrated Math 2
Integrated Math 3

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

Modeling Prompts

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15
Lesson 16
Lesson 17
Lesson 18

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Unit 5, Lesson 2

Representations of Growth and Decay (Optional)

Algebra 2

Practice

Problem 1

Student Task Statement

A home is purchased for $170,000. Since then, its value has increased 5% per year.

What is the approximate value of the home 3 years after it was purchased?
Write an equation, in function notation, to represent the value of the home as a function of time in years since it was purchased, .
Will the value of the home be more than $500,000 30 years after it was purchased (assuming that the trend continues)? Show your reasoning.

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Problem 2

Student Task Statement

The graph shows a wolf population that has been growing exponentially.

What was the population when it was first measured?
By what factor did the population grow in the first year?
Write an equation relating the wolf population, , and the number of years since it was measured, .

<p>Coordinate plane, x, 0 to 4 by 1, y, 0 to 200 by 40. Curve drawn through 0 comma 100, 1 comma 120.</p>

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Problem 3

Student Task Statement

Here is the graph of an exponential function .

<p>Coordinate plane, x, 0 to 4 by 1, y, 0 to 800 by 200. Curve starts on the y-axis between 0 and 100, goes through 1 comma 100, 2 comma 200, 3 comma 400, 4 comma 800.</p>

Find an equation defining . Explain your reasoning.

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Problem 4

Student Task Statement

The equation represents the value of a car, in dollars, years after it was purchased.

What do the numbers 24,500 and 0.88 mean?
What does represent?
Sketch a graph that represents the function and shows and .

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Problem 5

ForLesson 1: Growing and Shrinking

Student Task Statement

The first two terms of an exponential sequence are 18 and 6. What are the next 3 terms of this sequence?

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Problem 6

ForLesson 1: Growing and Shrinking

Student Task Statement

A bacteria population has been doubling each day for the last 5 days. It is currently 100,000. What was the bacterial population 5 days ago? Explain how you know.

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Problem 7

ForLesson 3: Exponents That Are Unit Fractions

Student Task Statement

Select all expressions that are equivalent to .

9
3

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Lesson 2 Resources

Student Materials