Question

In 2006, a laptop computer was purchased for $2000. Each year since, the resale value has decreased by 22%.

Let t be the number of years since 2006. Let y be the value of the laptop computer, in dollars.
Write an exponential function showing the relationship between y and t.

Answer 1

Answer: y = 2000(0.78)^t

This is the same as writing
`y = 2000(0.78)^t`

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Step-by-step explanation:

The answer above is in the form y = a*b^t

a = initial price = 2000 dollars

b = decay factor = 0.78

We have a decay factor because 0 < b < 1 and because the price decreases. The 0.78 is from the computation of 1 - 0.22 = 0.78

Meaning that if the price goes down 22%, then we keep the remaining 78%

So each year, the laptop keeps 78% of its previous price after losing 22%.