a new car is purchased for 17900 dollars. the value of the car depreciates at 13% per year. what will the…

a new car is purchased for 17900 dollars. the value of the car depreciates at 13% per year. what will the value of the car be, to the nearest cent, after 7 years?

a new car is purchased for 17900 dollars. the value of the car depreciates at 13% per year. what will the value of the car be, to the nearest cent, after 7 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 decay as a decimal, and $t$ is the time in years.

Step2: Convert the rate to a decimal

The rate of depreciation $r = 13%=0.13$, the initial value $P = 17900$, and the time $t = 7$.

Step3: Substitute the values into the formula

$A=17900\times(1 - 0.13)^7=17900\times(0.87)^7$.

Step4: Calculate $(0.87)^7$

$(0.87)^7=0.87\times0.87\times0.87\times0.87\times0.87\times0.87\times0.87\approx0.377149$.

Step5: Calculate the final value of the car

$A = 17900\times0.377149\approx6750.97$.

Answer:

$6750.97$