Question

a car is purchased for $26,000. after each year, the resale value decreases by 20%. what will the resale value be after 4 years? use the calculator provided and round your answer to the nearest dollar.

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 (or initial value), $r$ is the rate of decrease (in decimal), and $t$ is the time in years.
Here, $P = 26000$, $r = 0.20$ (since 20% = 0.20), and $t = 4$.

Step2: Substitute the values into the formula

First, calculate $(1 - r)$: $1 - 0.20 = 0.80$.
Then, raise this to the power of $t$: $0.80^4$. Let's calculate $0.80^4$: $0.80\times0.80 = 0.64$; $0.64\times0.80 = 0.512$; $0.512\times0.80 = 0.4096$.
Now, multiply by $P$: $V = 26000\times0.4096$.

Step3: Calculate the final value

$26000\times0.4096 = 10649.6$. Rounding to the nearest dollar gives $10650$.

Answer:

10650