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.

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is $A = P(1 - r)^t$, where:

• $A$ is the final amount,
• $P$ is the initial principal amount,
• $r$ is the rate of decay (in decimal),
• $t$ is the time in years.

Here, $P = 43330$, $r = 0.17$ (since 17% = 0.17), and $t = 9$.

Step2: Substitute the values into the formula

Substitute $P = 43330$, $r = 0.17$, and $t = 9$ into the formula:
$A = 43330(1 - 0.17)^9$

Step3: Calculate $(1 - 0.17)$

First, calculate $1 - 0.17 = 0.83$.

Step4: Calculate $0.83^9$

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

Step5: Multiply by the initial amount

Multiply $43330$ by $0.1986$:
$A = 43330 \times 0.1986 \approx 8605.34$

Answer:

$\$8605.34$