Question

The cost of High Definition television now averages $1200, but the cost is

decreasing by about 15% percent per year. What will the cost be in 7
years? *

Answer 1

The cost in 7 years will be of $384.69.

Explanation:

Equation for exponential decay:

The equation for an amount after t years is given by:

`A(t) = A(0)(1-r)^t`

In which A(0) is the initial value and r is the decay rate.

The cost of High Definition television now averages $1200, but the cost is decreasing by about 15% percent per year.

This means that
`A(0) = 1200, r = 0.15`. So

`A(t) = A(0)(1-r)^t`

`A(t) = 1200(1-0.15)^t`

`A(t) = 1200(0.85)^t`

What will the cost be in 7 years?

This is A(7).

`A(t) = 1200(0.85)^t`

`A(7) = 1200(0.85)^7 = 384.69`

The cost in 7 years will be of $384.69.