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=\frac{\ln(100)}{\ln(375)}\Rightarrow t\approx0.8$

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