Answer to Question #168971 in Algebra for Alex

Question

The value of a truck bought new for $28,000 depreciates 9.5% each year. Write the exponential function then determine the value of the truck after 7 years.

Answer 1

The value of a truck in general is

$C_n = C_0 b^n$

where

$C_0$ - initial value

b - decay factor

n - number of periods

In this problem

$C_0 = 28,000$

b = 100% - 9.5% = 90.5% = 0.905

Exponential function is

$C_n = 28,000*0.905^n$

The value of the truck after 7 years:

$C_7 = 28,000 * 0.905^7 \approx 13,921.89$