Question

A laptop computer was purchased for $1250. Each year since, the resale value has decreased by 22%. 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

Answer 1

y = 1250 - .22t

Answer 2

To write an exponential function showing the relationship between the resale value y and the number of years since the purchase t, we can use the formula:

y = P(1 - r)^t

Where:
P is the initial value (purchase price) of the laptop computer
r is the rate of decrease (as a decimal)
t is the number of years since the purchase

In this case, the initial value P is $1250 and the rate of decrease r is 22%, which can be expressed as 0.22.

Substituting these values into the formula, we get:

y = $1250(1 - 0.22)^t

Simplifying further, we have:

y = $1250(0.78)^t

Therefore, the exponential function showing the relationship between the resale value y and the number of years since the purchase t is y = $1250(0.78)^t.