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

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

`f(x) = 32,500 * \left(0.88\right)^x`

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 + (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 - (12)/(100) \right)^x = 32,500 \cdot \left(0.88\right)^x`