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? answer attempt 1 out of 2

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 attempt 1 out of 2

Answer

Explanation:

Step1: Identify the depreciation - formula

The formula for exponential depreciation 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 number of years. Here, $P=$17000$, $r = 0.1225$, and $t = 14$.

Step2: Substitute the values into the formula

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

Step3: Calculate $(0.8775)^{14}$

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

Step4: Calculate the value of the car $A$

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

Answer:

$2852.09$