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

question 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?

question 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 depreciation as a decimal, and $t$ is the number of years. Here, $P=$17900$, $r = 0.13$, and $t = 7$.

Step2: Substitute the values into the formula

$A=17900\times(1 - 0.13)^7$. First, calculate $1-0.13 = 0.87$. Then, find $(0.87)^7$. $(0.87)^7=0.87\times0.87\times0.87\times0.87\times0.87\times0.87\times0.87\approx0.377149$.

Step3: Calculate the final value of the car

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

Answer:

$6750.97$