a new car is purchased for 18000 dollars. the value of the car depreciates at 13.5% per year. what will the…

a new car is purchased for 18000 dollars. the value of the car depreciates at 13.5% per year. what will the value of the car be, to the nearest cent, after 14 years?

a new car is purchased for 18000 dollars. the value of the car depreciates at 13.5% 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 number of years. Here, $P=$18000$, $r = 0.135$, and $t = 14$.

Step2: Substitute the values into the formula

$A=18000\times(1 - 0.135)^{14}$. First, calculate $1-0.135 = 0.865$. Then we have $A = 18000\times(0.865)^{14}$.

Step3: Calculate $(0.865)^{14}$

Using a calculator, $(0.865)^{14}\approx0.15777$.

Step4: Calculate the value of $A$

$A = 18000\times0.15777=2839.86$.

Answer:

$2839.86$