Depreciating phone

Question

Suppose that a phone that originally sold for $800 loses 3/5 of its value each year after it is released.

1. After 2 years, how much is the phone worth?

2. Write an equation for the value of the phone, p, t years after it is released.

Answer 1

The phone loses 60% of its value every year.

After the first year, the phone is worth 800(1-.6) =800(.4) = 320.

After the second year it is worth 320(.4) = 800(.4)(.4) = 128

After the third year it is worth 128(.4) = 800(.4)(.4)(.4) = 51.20

and so on.

so p = 800(.4)^t

1. p(2) = 800(.4)² = 128
2. p(t) = 800(.4)^t