# 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?

May 31, 2016

2 item retained after $2 \frac{1}{2}$ hours

#### Explanation:

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

Then $i = k \times \frac{1}{t}$

Given condition is $i = 20 \text{ and } t = \frac{1}{4} = 0.25$

$\implies 20 = k \times \frac{1}{0.25}$

Multiply both sides by 0.25

$\implies 20 \times 0.25 = k \times \frac{0.25}{0.25}$

But $\frac{0.25}{0.25} = 1$

$5 = k$

Thus: color(brown)(i=kxx1/tcolor(blue)(-> i =k/t = 5/t
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Thus after $t = 2.5$

$i = \frac{5}{2.5} = 2$