Question

The value of a piece of factory equipment was $20,000 when it was purchased. During each 1-year period after the equipment was purchased, the value of the equipment at the end of the period was 10% less than its value at the beginning of the period. Which of the following statements identifies the most appropriate type of function to model this scenario and provides a reason to support its appropriateness?


Option A,A linear function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was $10 less than its value 1 year before.


Option B,A linear function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was $2,000 less than its value 1 year before.


Option C,An exponential function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was 0.1 times its value 1 year before.


Option D,An exponential function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was 0.9 times its value 1 year before.

Answer 1

Answer: Option D.

Reason: The value is reduced by a constant percentage (10%) each year, so each year it equals 0.9 times the previous year's value. That is multiplicative decay and is modeled by an exponential function V(n) = 20,000*(0.9)^n. Options A and B describe a fixed dollar decrease (linear) which is false, and C incorrectly states the remaining factor is 0.1 instead of 0.9.