a car enthusiast learns that a particular mod...
a car enthusiast learns that a particular model of car, which costs $34,411 new, loses 25% of its value every year. how much will the car be worth in 6 years? if necessary, round your answer to the nearest cent.
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, $P=\$34411$, $r = 0.25$, and $t = 6$.
## Step2: Substitute the values into the formula
$A=34411\times(1 - 0.25)^6$.
First, calculate $(1 - 0.25)=0.75$. Then, find $0.75^6=0.75\times0.75\times0.75\times0.75\times0.75\times0.75\approx0.1779785$.
## Step3: Calculate the final value
$A = 34411\times0.1779785\approx6127.31$.
# Answer:
$6127.31$