question\na new car is purchased for 15300 dollars. the value of the car depreciates at 14.25% per year…

question\na new car is purchased for 15300 dollars. the value of the car depreciates at 14.25% per year. what will the value of the car be, to the nearest cent, after 6 years?

question\na new car is purchased for 15300 dollars. the value of the car depreciates at 14.25% 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 as a decimal, and $t$ is the number of years. Here, $P=$15300$, $r = 0.1425$, and $t = 6$.

Step2: Substitute the values into the formula

$A=15300\times(1 - 0.1425)^{6}$. First, calculate $1-0.1425 = 0.8575$. Then, find $(0.8575)^{6}$. $(0.8575)^{6}=0.8575\times0.8575\times0.8575\times0.8575\times0.8575\times0.8575\approx0.3777$.

Step3: Calculate the final value

$A = 15300\times0.3777$. $A=15300\times0.3777 = 5778.81$.

Answer:

$5778.81$