question a new car is purchased for 16200 dollars. the value of the car depreciates at 14.25% per year. what…

question a new car is purchased for 16200 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 attempt 1 out of 10

question a new car is purchased for 16200 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 attempt 1 out of 10

Answer

Explanation:

Step1: Identify the depreciation formula

The formula for exponential - decay (depreciation) is $A = P(1 - r)^t$, where $P$ is the initial value, $r$ is the rate of depreciation per year as a decimal, and $t$ is the number of years. Here, $P=$16200$, $r = 0.1425$, and $t = 6$.

Step2: Substitute the values into the formula

$A=16200\times(1 - 0.1425)^6$. First, calculate $1-0.1425 = 0.8575$. Then, calculate $(0.8575)^6$. $(0.8575)^6=0.8575\times0.8575\times0.8575\times0.8575\times0.8575\times0.8575\approx0.3777$. Next, multiply by the initial value: $A = 16200\times0.3777$. $A=16200\times0.3777 = 6118.74$.

Answer:

$6118.74$