Analyzing Graphs

ID: nukut-fufis
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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2
Grade: 8-9
Standards: 8.EE.A.1HSF-IF.B.4HSF-BF.A.1HSA-CED.A.2
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11 questions

Analyzing Graphs

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Fractions and Decimals

In the table, find as many patterns as you can. Use one or more patterns to help you complete the table. Write the values for the labeled cells in the answer boxes below.

fraction121418116132decimal0.50.250.125AB\begin{array}{|c|c|c|c|c|c|} \hline \\[-1em] \textbf{fraction} & \frac{1}{2} & \frac{1}{4} & \frac{1}{8} & \frac{1}{16} & \frac{1}{32} \\[-1em] \\ \hline \\[-1em] \textbf{decimal} & 0.5 & 0.25 & 0.125 & \text{A} & \text{B} \\[-1em] \\ \hline \end{array}

1) Cell A

2) Cell B

3) Explain your reasoning.

Falling and Falling

The value of some cell phones changes exponentially after initial release. Here are graphs showing the depreciation of two phones 1, 2, and 3 years after they were released.

A template for answering this question. Ask your instructor for an alternative.

4) Which phone is more expensive to buy when it is first released?

5) How does the value of each phone change with every passing year?

6) Which one is falling in value more quickly?

7) Explain or show how you know.

8) If the phones continue to depreciate by the same factor each year, what will the value of phone A be 4 years after its initial release?

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9) If the phones continue to depreciate by the same factor each year, what will the value of phone B be 4 years after its initial release?

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10) For cell phone A, write an equation that relates the value of the phone in dollars to the years since release, tt. Use vv for the value of Phone A.

11) For cell phone B, write an equation that relates the value of the phone in dollars to the years since release, tt. Use ww for the value of Phone B.