Question

a car enthusiast learns that a particular model of car, which costs $43,330 new, loses 17% of its value every year. how much will the car be worth in 9 years? if necessary, round your answer to the nearest cent. $ submit

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is $V = P(1 - r)^t$, where $V$ is the final value, $P$ is the initial principal (value), $r$ is the rate of decay (as a decimal), and $t$ is the time in years.

Step2: Plug in the given values

Here, $P = 43330$, $r = 0.17$ (since 17% = 0.17), and $t = 9$. So we calculate $V = 43330(1 - 0.17)^9$.

Step3: Calculate $(1 - 0.17)$

$1 - 0.17 = 0.83$.

Step4: Calculate $0.83^9$

Using a calculator, $0.83^9 \approx 0.1986$.

Step5: Multiply by the initial value

$V = 43330\times0.1986 \approx 8605.34$.

Answer:

$\$8605.34$