a vehicle purchased for $32500 depreciates at a rate of 7% per year. determine the approximate value of the…

Explanation:

Step1: Identify the depreciation formula

The formula for exponential - decay is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ 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

Given $r = 7%=0.07$, $P=$32500$, and $t = 13$ years.

Step3: Substitute the values into the formula

$A=32500\times(1 - 0.07)^{13}=32500\times(0.93)^{13}$.

Step4: Calculate $(0.93)^{13}$

$(0.93)^{13}\approx0.4087$.

Step5: Calculate the final value of the vehicle

$A = 32500\times0.4087=32500\times0.4087 = 13292.75$.

Step6: Round to the nearest whole number

Rounding $13292.75$ to the nearest whole number gives $13293$.

Answer:

$13293$