Question

Instructions: Interpret the function given in the context ofthe real-world situation described to answer the question.Nichole bought a new car. The depreciation equation isgiven by f(x) = 27,000(.86), where a representsthe number of years since the purchase of the car, andf(x) represents the value of the car. By what percentdoes Nichole's car depreciate each year?%

Answer 1

The depreciation equation is given by

$f(x)=27000(0.86^x)$

where x represents the number of years. Here, the initial value of the car corresponds to x=0, then we have

$\text{ initial value = f\lparen0\rparen=27000}$

After one year, the car value corresponds to x=1, that is,

$\text{ after 1 year = f\lparen1\rparen=27000\lparen0.86}\rparen^1\text{=27000}\times0.86=\text{23220}$

Now, let's find the depreciation percentage by means of a rule of three:

$\begin{gathered} 2700\text{ ----- 100 \%} \\ 23220\text{ ------- x} \end{gathered}$

so we have

$x=\frac{23220\times100}{27000}=86\text{ \%}$

So the difference between 100% and 86% is 14% This means Nichole's car depreciate 14% each year