a car enthusiast learns that a particular model of car, which costs $34,411 new, loses 25% of its value…

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.

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:

$6127.31$