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Quantities that Change Exponentially

5.7.4 Quantities that Change Exponentially

5.7.4 • Quantities that Change Exponentially

Cool Down

Scatter plot showing a steep decline in value (dollars) over time (years) from about $700 at year 1 to near $0 by year 10, indicating rapid decrease followed by stabilization.
1.

This graph represents one of the following descriptions. Which one?

a. A phone loses 4 5 4 5 of its value every year after purchase; the relationship between the number of years since purchasing the phone and the value of the phone.

b. The number of stores a company has tripled approximately every 5 years; the relationship between the number of years and the number of stores.

c. A camera loses 2 5 2 5 of its value every year after purchase; the relationship between the number of years since purchasing the camera and the value of the camera.

Compare your answer:

A camera loses 2 5 2 5 of its value every year after purchase; the relationship between the number of years since purchasing the camera and the value of the camera.

2.

Explain how you know the graph represents the description you chose.

Your answers may vary, but here are some examples:

  • The graph cannot represent Description A because the phone is retaining only 1 5 1 5 of its value, which is less than half, and the vertical coordinate of the second point on the graph is more than half of the vertical intercept.
  • If the camera loses 2 5 2 5 of its value each year, then its value is 3 5 3 5 that of the previous year. The vertical intercept seems to be 1,200, and 3 5 3 5 of 1,200 is about 700, which is roughly the vertical coordinate of the second point.