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?

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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?

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Answer 1 · 2016-05-31T22:06:09

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

Explanation:

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

Then $i = k \times \frac{1}{t}$ $i=kxx1/t$

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

$\Rightarrow 20 = k \times \frac{1}{0.25}$ $=>20=kxx1/0.25$

Multiply both sides by 0.25

$\Rightarrow 20 \times 0.25 = k \times \frac{0.25}{0.25}$ $=>20xx0.25=kxx0.25/0.25$

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

$5 = k$ $5=k$

Thus: $i = k \times \frac{1}{t} \to i = \frac{k}{t} = \frac{5}{t}$ $color(brown)(i=kxx1/tcolor(blue)(-> i =k/t = 5/t$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Thus after $t = 2.5$ $t= 2.5$

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

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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?

1 Answer

Explanation:

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