a new car is purchased for 24500 dollars. the value of the car depreciates at 14.75% per year. what will the…

a new car is purchased for 24500 dollars. the value of the car depreciates at 14.75% per year. what will the value of the car be, to the nearest cent, after 14 years?

a new car is purchased for 24500 dollars. the value of the car depreciates at 14.75% per year. what will the value of the car be, to the nearest cent, after 14 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, and $t$ is the time in years. Here, $P=$24500$, $r = 0.1475$, and $t = 14$.

Step2: Substitute the values into the formula

$A=24500\times(1 - 0.1475)^{14}$. First, calculate $1-0.1475 = 0.8525$. Then, find $(0.8525)^{14}$. Using a calculator, $(0.8525)^{14}\approx0.13977$.

Step3: Calculate the final value

$A = 24500\times0.13977$. $A\approx3424.37$.

Answer:

$3424.37$