question a new car is purchased for 19000 dollars. the value of the car depreciates at 11.25% per year. what…

question a new car is purchased for 19000 dollars. the value of the car depreciates at 11.25% per year. what will the value of the car be, to the nearest cent, after 14 years?

question a new car is purchased for 19000 dollars. the value of the car depreciates at 11.25% 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 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 $r = 11.25%=0.1125$, $P = 19000$, and $t = 14$.

Step3: Substitute the values into the formula

$A=19000\times(1 - 0.1125)^{14}$. First, calculate $1-0.1125 = 0.8875$. Then, calculate $(0.8875)^{14}$. Using a calculator, $(0.8875)^{14}\approx0.19077$. Next, multiply by the initial amount: $A = 19000\times0.19077 = 3624.63$.

Answer:

$3624.63$