Question

The price of a computer component is decreasing at a rate of 12% per year. If the component costs $50 today, what will it cost in 3 years?

Answer 1

`\bf \qquad \textit{Amount for Exponential change}\\\\ A=P(1\pm r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{starting amount}\to &50\\ r=rate\to 12\%\to (12)/(100)\to &0.12\\ t=\textit{elapsed period}\to &3\\ \end{cases} \\\\\\ A=50(1-0.12)^3`

Answer 2

The cost of the computer in 3 years is $34.07

Explanation:

We have formula for depreciation.

`P = P_0(1 - (r)/(100) )^n`

Where P is the final value, P_0 = initial value , r = rate of decrease and n = the number of years.

Given: P_0 = $50, r = 12 and n = 3

Now plug in the given values in the above formula, we get

`P = 50(1 - (12)/(100) )^3`

`P = 50(1 - 0.12)^3`

P =
`50(0.88)^3`

P = $34.07

Therefore, the cost of the computer in 3 years is $34.07