IM Alg1.5.6 Lesson: Analyzing Graphs
In the table, find as many patterns as you can. Use one or more patterns to help you complete the table. Be prepared to explain your reasoning.
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.
Which phone is more expensive to buy when it is first released?
How does the value of each phone change with every passing year?
Which one is falling in value more quickly? Explain or show how you know.
If the phones continue to depreciate by the same factor each year, what will the value of each phone be 4 years after its initial release?
For each cell phone, write an equation that relates the value of the phone in dollars to the years since release, . Use for the value of Phone A and for the value of Phone B.
When given data, it is not always clear how to best model it. In this case we were told the value of the cell phones was changing exponentially. Suppose, however, we were instead just given the initial values of the the cell phones when released and the values after each of the first three years. Use technology to compute the best fit line for each cell phone. Round any numbers to the nearest dollar.
Explain why, in this situation, an exponential model might be more appropriate than the linear model you just created.