a new car is purchased for 22300 dollars. the value of the car depreciates at 10.25% per year. what will the…

a new car is purchased for 22300 dollars. the value of the car depreciates at 10.25% per year. what will the value of the car be, to the nearest cent, after 6 years?

a new car is purchased for 22300 dollars. the value of the car depreciates at 10.25% per year. what will the value of the car be, to the nearest cent, after 6 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=$22300$, $r = 0.1025$, and $t = 6$.

Step2: Substitute the values into the formula

$A=22300\times(1 - 0.1025)^6$. First, calculate $1-0.1025 = 0.8975$. Then, find $(0.8975)^6$. $(0.8975)^6=0.8975\times0.8975\times0.8975\times0.8975\times0.8975\times0.8975\approx0.53177$.

Step3: Calculate the final value

$A = 22300\times0.53177$. $A\approx22300\times0.53177 = 11858.471\approx11858.47$.

Answer:

$11858.47$