A rumour spreads through a population in such a way that t hours after the rumour starts.... ...the percent of people involved in passing it on is given by P(t)=100(e^-t - e^-4t). What is the highest percent of people involved in spreading the rumour within the first 3 hours? When does this occur?

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`P(t) = 100(e^-t-e^(-4t))`

To find the maximum percentage we first find the critical points when `(dP(t))/(dt) =0`

`(dP(t))/(dt) = 100(-e^-t+4e^(-4t)) = 0`

We divide both sides by 100 and move the `e^-t` to the other side...

(The entire section contains 112 words.)

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