a new car is purchased for 17000 dollars. the value of the car depreciates at 13.5% per year. what will the…

a new car is purchased for 17000 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 12 years?

a new car is purchased for 17000 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 12 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=$17000$, $r = 0.135$, and $t = 12$.

Step2: Substitute the values into the formula

$A=17000\times(1 - 0.135)^{12}$ $A = 17000\times(0.865)^{12}$

Step3: Calculate $(0.865)^{12}$

$(0.865)^{12}\approx0.18477$

Step4: Calculate the value of $A$

$A=17000\times0.18477$ $A = 3141.09$

Answer:

$3141.09$