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9-12 Integrated Math 3 Unit 4 Lesson 2

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K-5 Math 6-8 Math •9-12 Math

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Unit 4, Lesson 2

Representations of Growth and Decay (Optional)

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Integrated Math 3

Practice

Problem 1

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, \(t\).
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

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, \(w\), and the number of years since it was measured, \(t\).

<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

Here is the graph of an exponential function \(f\).

<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 \(f\). Explain your reasoning.

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Problem 4

The equation \(f(t) = 24,\!500 \boldcdot (0.88)^t\) represents the value of a car, in dollars, \(t\) years after it was purchased.

What do the numbers 24,500 and 0.88 mean?
What does \(f(9)\) represent?
Sketch a graph that represents the function \(f\) and shows \(f(0), \) \(f(1),\) and \(f(2)\).

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Problem 5

ForLesson 1: Growing and Shrinking

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

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

from an earlier course

Select all expressions that are equivalent to \(27^{\frac13}\).

9
3
\(\sqrt{27}\)
\(\sqrt[3]{27}\)
\(\sqrt[3]{3^3}\)
\(\frac{1}{27}\)
\(\frac{1}{27^3}\)

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Lesson 2 Resources

Student Materials