Question

a laptop computer is purchased for $2350. after each year, the resale value decreases by 30%. 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 depreciation

The formula for exponential depreciation is $V = P(1 - r)^t$, where $V$ is the final value, $P$ is the initial principal (purchase price), $r$ is the rate of depreciation (as a decimal), and $t$ is the time in years.
Here, $P = 2350$, $r = 0.30$ (since 30% = 0.30), and $t = 4$.

Step2: Substitute the values into the formula

Substitute the values into the formula: $V = 2350(1 - 0.30)^4$.
First, calculate $(1 - 0.30) = 0.70$. Then, raise 0.70 to the power of 4: $0.70^4 = 0.70\times0.70\times0.70\times0.70 = 0.2401$.

Step3: Calculate the final value

Multiply the initial price by the result from Step 2: $V = 2350\times0.2401$.
$2350\times0.2401 = 2350\times0.2401 = 564.235$.

Step4: Round to the nearest dollar

Rounding 564.235 to the nearest dollar gives 564.

Answer:

The resale value after 4 years is $\$564$.