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9-12 Algebra 1 Unit 6 Lesson 12

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Unit 6, Lesson 12

Reasoning about Exponential Graphs (Part 1)

Algebra 1

Practice

Problem 1

Student Task Statement

Here are equations defining three exponential functions , , and .

Which of these functions grows the least quickly? Which one grows the most quickly? Explain how you know.
The three given graphs represent , , and . Which graph corresponds to each function?

Graph of three increasing exponential functions, xy-plane, origin O. Horizontal axis, scale 0 to 3, by 1’s. Vertical axis, scale 0 to 6,000, by 1,000’s. Function C is red and has these points: (0 comma 100), (1 comma 300), (2 comma 900) and (3 comma 2,700). Function A is blue and has these points: (0 comma 100), (1 comma 400), (2 comma 1600) and (3 comma 6,400). Function B is green and has these points: (0 comma 100), (1 comma 350), (2 comma 1,225) and (3 comma 4,287 point 5.
Why do all three graphs share the same intersection point with the vertical axis?

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Problem 2

Student Task Statement

Here are graphs of three exponential equations.

Match each equation with its graph.

<p>Graph of three increasing exponential functions, xy-plane, origin O.</p>

K
L
M

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Problem 3

Student Task Statement

The function is given by , and the function is given by . The graph of is labeled and the graph of is labeled .

If is the graph of and is defined by , what can you say about and ? Explain your reasoning.

<p>Graph of three lines.</p>

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Problem 4

Student Task Statement

Here is a graph of .

On the same coordinate plane:

Sketch a graph of and label it .
Sketch a graph of and label it .

<p>Graph of line, origin O. Horizontal axis 0 to 3, by 1’s, labeled x. Vertical from 0 to 900, by 100’s, labeled y. Line starts at 0 comma 100, passes through 1 comma 200, 2 comma 400, 3 comma 800.<br>
</p>

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Problem 5

ForLesson 4: Graphing Linear Inequalities in Two Variables (Part 1)

Student Task Statement

Choose the inequality whose solution region is represented by this graph.

<p>Inequality graphed on a coordinate plane, origin O. Each axis from negative 4 to 4, by 2’s. Solid line goes through negative 4 comma negative 6, 0 comma negative 3, and 4 comma 0. The region above the solid line is shaded.</p>

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Problem 6

ForLesson 4: Representing Exponential Decay

Student Task Statement

Technology required. Start with a square with an area of 1 square unit (not shown). Subdivide it into 9 squares of equal area and remove the middle one to get the first figure shown.

<p>4 figures showing construction of a pattern.</p>

What is the area of the first figure shown (Stage 1)?
Take the remaining 8 squares, subdivide each into 9 equal squares, and remove the middle one from each. What is the area of the figure now (Stage 2)?
Continue the process and find the area for Stages 3 and 4.
Write an equation representing the area at Stage .
Use technology to graph your equation.
Use your graph to find the first stage when the area is first less than square unit.

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Problem 7

ForLesson 10: Looking at Rates of Change

Student Task Statement

The equation gives the balance of a bank account years since the account was opened. The graph shows the annual account balance for 10 years.

What is the average annual rate of change for the bank account?
Is the average rate of change a good measure of how the bank account varies during this time period? Explain your reasoning.

<p>Graph of function.</p>

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Lesson 12 Resources

Student Materials Student Materials in Spanish