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

$948.15

Step-by-step 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*(1-(1)/(3))^{(t)/(2)} \\ f(t)=3200*((2)/(3))^{(t)/(2)} \end{gathered}`

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

`\begin{gathered} f(6)=3200*((2)/(3))^{(6)/(2)} \\ =3200*((2)/(3))^3 \\ =3200*(8)/(27) \\ =\$948.15 \end{gathered}`

The computer will be worth $948.15 in 6 years.