Question

a laptop computer was purchased for $1600. each year since, the resale value has decreased by 27%. let t be the number of years since the purchase. let y be the resale value of the laptop computer, in dollars. write an exponential function showing the relationship between y and t.

Explanation:

Step1: Define decay factor

Since the value decreases by 27% annually, the remaining value percentage is $100\% - 27\% = 73\%$, or $0.73$ in decimal form.

Step2: Set up exponential model

The initial value $a = 1600$, decay factor $b = 0.73$. The general exponential decay formula is $y = a \cdot b^t$.
Substitute the known values:
$y = 1600 \cdot (0.73)^t$

Answer:

$y = 1600(0.73)^t$