Question

You buy a video game console for $500 and it depreciates at a rate of 25%. How long wait take for the video me conode to be worth $100 Round your answer to the nearest tenth (one decimal place)

Answer 1

We will determine the time it takes as follows:

We have to follow the expression:

`y=a(1-p)^t`

Here y is the value to obtain, a is the original value, p is the percentage and t is the time it takes:

Now, we solve for t:

`100=500(1-0.25)^t\Rightarrow\ln (100)=t\ln (500(0.75))`
`\Rightarrow t=(\ln(100))/(\ln(375))\Rightarrow t\approx0.8`

It will take 0.8 units of time [Since there are no units given].