a new car is purchased for 16400 dollars. the value of the car depreciates at 12.5% per year. what will the…

a new car is purchased for 16400 dollars. the value of the car depreciates at 12.5% per year. what will the value of the car be, to the nearest cent, after 8 years? answer attempt 1 out of 5

a new car is purchased for 16400 dollars. the value of the car depreciates at 12.5% per year. what will the value of the car be, to the nearest cent, after 8 years? answer attempt 1 out of 5

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, and $t$ is the time in years.

Step2: Substitute the given values

Here, $P=$16400$, $r = 0.125$ (since $12.5%=0.125$), and $t = 8$. So, $A=16400\times(1 - 0.125)^8$.

Step3: Calculate the value inside the parentheses

$1-0.125 = 0.875$.

Step4: Calculate the power

$(0.875)^8=0.875\times0.875\times0.875\times0.875\times0.875\times0.875\times0.875\times0.875\approx0.3404$.

Step5: Calculate the final value of the car

$A = 16400\times0.3404\approx5572.56$.

Answer:

$5572.56$