Question

It is estimated that a computer loses a third of its value every 2 years. If youbuy a computer for $3200, how much will the computer be worth in 6 years?(round your answer to the nearest hundredth)What is the equation of the function?

Answer 1

Answer:

$948.15

Explanation:

Initial Value of the computer = $3200

If the computer loses a third of its value every 2 years, the function for its value after t years is given as:

$\begin{gathered} f(t)=3200\times(1-\frac{1}{3})^{\frac{t}{2}} \\ f(t)=3200\times(\frac{2}{3})^{\frac{t}{2}} \end{gathered}$

Therefore, the worth of the computer 6 years after will be:

$\begin{gathered} f(6)=3200\times(\frac{2}{3})^{\frac{6}{2}} \\ =3200\times(\frac{2}{3})^3 \\ =3200\times\frac{8}{27} \\ =\ 948.15 \end{gathered}$

The computer will be worth $948.15 in 6 years.