Analyzing Graphs

ID: nukut-fufis
Illustrative Mathematics, CC BY 4.0
Subject: Algebra, Algebra 2
Standards: 8.EE.A.1HSF-IF.B.4HSF-BF.A.1HSA-CED.A.2

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.

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

1) Cell A

2) Cell B

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.

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?

Show Work

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?

Show Work

10) For cell phone A, write an equation that relates the value of the phone in dollars to the years since release, ﻿$t$﻿. Use ﻿$v$﻿ 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, ﻿$t$﻿. Use ﻿$w$﻿ for the value of Phone B.