The value of some cell phones changes exponentially after initial release. Here are graphs showing the depreciation of two phones 1, 2, 3 and 4 years after they were released.

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  1. Which phone is more expensive to buy when it is first released?
  2. How does the value of each phone change with every passing year?
  3. Which one is falling in value more quickly? Explain or show how you know.
  4. 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?
  5. For each cell phone, 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 and w for the value of Phone B.

Sangeetha Pulapaka
  1. Phone A was expensive when it was first released. It was $1000 when at 0 years.
  2. Phone A decreases by a common decay factor of 0.8 or \frac{4}{5} and Phone B decreases by 0.5 or \frac{1}{2}
  3. Phone B falls in value more quickly as the smaller fraction decays faster.
  4. If both the phones were to depreciate by a factor of 0.5 each year, then phone A would be 62.5 dollars at 4 years, and phone B is 52.
  5. v = 1000 \cdot\Big( \frac{4}{5}\Big)^{d} is the value of phone A and w = 840 \cdot \Big (\frac{1}{2}\Big)^{d} is the value of phone B.