Question

The amount of information retained varies inversely with the number of hours passed since the information was given. If Diana can retain 20 new vocabulary words 1/4 hour after she learns them, how many will she retain 2.5 hours after she reads them?

Answer 1

2 item retained after `2 1/2` hours

Explanation:

Let information be `i`
Let time be `t`
Let the constant of variation be `k`

Then `i=kxx1/t`

Given condition is `i= 20" and "t=1/4=0.25`

`=>20=kxx1/0.25`

Multiply both sides by 0.25

`=>20xx0.25=kxx0.25/0.25`

But `0.25/0.25=1`

`5=k`

Thus: `color(brown)(i=kxx1/tcolor(blue)(-> i =k/t = 5/t`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Thus after `t= 2.5`

`i=5/2.5 = 2`