Question

a laptop computer is purchased for $950. after each year, the resale value decreases by 25%. what will the resale value be after 3 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 $A = P(1 - r)^t$, where $P$ is the initial amount, $r$ is the rate of decay, and $t$ is the time.
Here, $P = 950$, $r = 0.25$ (25% as a decimal), and $t = 3$.

Step2: Substitute the values into the formula

First, calculate $(1 - r)$: $1 - 0.25 = 0.75$.
Then, raise this to the power of $t$: $0.75^3$.
Calculate $0.75^3 = 0.75 \times 0.75 \times 0.75 = 0.421875$.
Now, multiply by $P$: $A = 950 \times 0.421875$.

Step3: Perform the multiplication

$950 \times 0.421875 = 400.78125$.

Step4: Round to the nearest dollar

Rounding $400.78125$ to the nearest dollar gives $401$.

Answer:

$401$