Question

in 2007, a laptop computer was purchased for $1450. each year since, the resale value has decreased by 24%. let t be the number of years since 2007. let y be the value of the laptop computer, in dollars. write an exponential function showing the relationship between y and t.

Explanation:

Step1: Identify initial value

The initial value (in 2007, when $t=0$) is $1450$, so $a=1450$.

Step2: Calculate decay factor

Since value decreases by 24%, the remaining value percentage is $100\%-24\%=76\%=0.76$, so the decay factor $b=0.76$.

Step3: Write exponential decay function

Use the exponential decay form $y = a(b)^t$.
$y = 1450(0.76)^t$

Answer:

$y = 1450(0.76)^t$