Question

chase buys a car for $31,556. his car immediately starts depreciating, losing 10% of its value every year. how much will the car be worth in 10 years? if necessary, round your answer to the nearest cent.

Explanation:

Step1: Identify the depreciation formula

The formula for exponential depreciation is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the rate of depreciation, and $t$ is the time in years.
Here, $P = 31556$, $r = 0.10$ (since 10% = 0.10), and $t = 10$.

Step2: Substitute the values into the formula

Substitute the values into $A = P(1 - r)^t$:
$A = 31556(1 - 0.10)^{10}$
First, calculate $(1 - 0.10) = 0.90$. Then, $0.90^{10} \approx 0.3486784401$.

Step3: Calculate the final amount

Multiply $31556$ by $0.3486784401$:
$A = 31556 \times 0.3486784401 \approx 11000.00$ (rounded to the nearest cent)

Answer:

$\$11000.00$