Question

Amrita bought a new delivery van for $32,500. The value of this van depreciates at a rate of 12% each year. Write a function f(x) to model the value of the van after x years of ownership.

Answer 1

Answer:

The function, f(x) to model the value of the van can be expressed as follows;

$f(x) = 32,500 \times \left(0.88\right)^x$

Step-by-step explanation:

From the question, we have;

The amount at which Amrita bought the new delivery van, PV = $32,500

The annual rate of depreciation of the van, r = -12% per year

The Future Value, f(x), of the van after x years of ownership can be given according to the following formula

$f(x) = PV \cdot \left(1 + \dfrac{r}{100} \right)^x$

Therefore, the function, f(x) to model the value of the van after 'x' years of ownership can be expressed as follows;

$f(x) = 32,500 \cdot \left(1 - \dfrac{12}{100} \right)^x = 32,500 \cdot \left(0.88\right)^x$