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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?

Respuesta :

[tex]\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 \frac{12}{100}\to &0.12\\ t=\textit{elapsed period}\to &3\\ \end{cases} \\\\\\ A=50(1-0.12)^3[/tex]

Answer:

The cost of the computer in 3 years is $34.07

Step-by-step explanation:

We have formula for depreciation.

[tex]P = P_0(1 - \frac{r}{100} )^n[/tex]

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

[tex]P = 50(1 - \frac{12}{100} )^3[/tex]

[tex]P = 50(1 - 0.12)^3[/tex]

P = [tex]50(0.88)^3[/tex]

P = $34.07

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