Question

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p(z)=32400(0.71)²
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The value of a car purchased in 2018 can be modeled by the
function below where z is the number of years since the car was
purchased.
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I
Fin
Explain what the growth or decay factor you identified in the
previous question means in this situation.
B

Answer 1

the car's estimated value in 2021 is approximately $16,080.72, which is about 49.7% (100% - 29% x 3) of its original value in 2018.

Explanation:

The growth or decay factor identified in the previous question (which is 0.71 in this case) represents the rate of depreciation of the car's value over time. In other words, the factor indicates the percentage of the original value that remains after each year.

Since the factor is less than 1 (0.71 is less than 1), this means that the car's value decreases over time. Specifically, the car loses approximately 29% (100% - 71%) of its value each year according to the given function.

For example, if the car was purchased in 2018 and we want to find its estimated value in 2021 (which is 3 years later), we can substitute z = 3 into the function:

p(3) = 32400(0.71)^2 ≈ 16,080.72

This means that the car's estimated value in 2021 is approximately $16,080.72, which is about 49.7% (100% - 29% x 3) of its original value in 2018.