a new car is purchased for 17000 dollars. the value of the car depreciates at 12.25% per year. what will the…

a new car is purchased for 17000 dollars. the value of the car depreciates at 12.25% per year. what will the value of the car be, to the nearest cent, after 14 years?

a new car is purchased for 17000 dollars. the value of the car depreciates at 12.25% per year. what will the value of the car be, to the nearest cent, after 14 years?

Answer

Explanation:

Step1: Identify the depreciation formula

The formula for exponential - decay is $A = P(1 - r)^t$, where $P$ is the initial value, $r$ is the rate of depreciation as a decimal, and $t$ is the time in years.

Step2: Convert the rate to a decimal

Given $r = 12.25%=0.1225$, $P = 17000$, and $t = 14$.

Step3: Substitute values into the formula

$A=17000\times(1 - 0.1225)^{14}=17000\times(0.8775)^{14}$.

Step4: Calculate $(0.8775)^{14}$

Using a calculator, $(0.8775)^{14}\approx0.16777$.

Step5: Calculate the final value of the car

$A = 17000\times0.16777 = 2852.09$.

Answer:

$2852.09$