a new car is purchased for 20000 dollars. the value of the car depreciates at 12.5% per year. what will the…

Explanation:

Step1: Identify the depreciation formula

The formula for exponential - decay is $A = P(1 - r)^t$, where $P$ is the initial amount, $r$ 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 $r = 12.5%=0.125$, the initial value of the car $P = 20000$ dollars, and the time $t = 11$ years.

Step3: Substitute the values into the formula

$A=20000\times(1 - 0.125)^{11}=20000\times(0.875)^{11}$.

Step4: Calculate $(0.875)^{11}$

$(0.875)^{11}\approx0.225094$.

Step5: Calculate the value of the car $A$

$A = 20000\times0.225094 = 4501.88$ dollars.

Answer:

$4501.88$