question\na new car is purchased for 18000 dollars. the value of the car depreciates at 13.5% per year. what…

question\na new car is purchased for 18000 dollars. the value of the car depreciates at 13.5% per year. what will the value of the car be, to the nearest cent, after 14 years?\nanswer attempt 1 out of 2\nsubmit answer

question\na new car is purchased for 18000 dollars. the value of the car depreciates at 13.5% per year. what will the value of the car be, to the nearest cent, after 14 years?\nanswer attempt 1 out of 2\nsubmit answer

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. Here, $P=$18000$, $r = 0.135$, and $t = 14$.

Step2: Substitute the values into the formula

$A=18000\times(1 - 0.135)^{14}$. First, calculate $1-0.135 = 0.865$. Then, find $(0.865)^{14}$. Using a calculator, $(0.865)^{14}\approx0.14777$.

Step3: Calculate the final value

$A = 18000\times0.14777=2659.86$.

Answer:

$2659.86$