Question

a new car is purchased for 15000 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 10 years?

Explanation:

Step1: Define depreciation formula

The formula for annual depreciation is $A = P(1 - r)^t$, where $P$ = initial value, $r$ = annual depreciation rate, $t$ = time in years.

Step2: Identify given values

$P = 12000$, $r = 0.125$, $t = 10$

Step3: Substitute values into formula

$A = 12000(1 - 0.125)^{10}$

Step4: Calculate the decay factor

$1 - 0.125 = 0.875$, so $A = 12000(0.875)^{10}$

Step5: Compute $(0.875)^{10}$

$(0.875)^{10} \approx 0.26307$

Step6: Find final value

$A \approx 12000 \times 0.26307$

Answer:

$3156.84$ dollars