Question

A certain rumor spreads through a community at the rate dy/dt= 2y(1−y) , where y is the proportion of the population that has heard the rumor at time t. At what time t is the rumor spreading the fastest?

Answer 1

1/2 or 50% of the population has heard the rumor when it is spreading fastest.

Explanation:

We need to take the derivative with respect to y from the r(y) = dy/dt = 2y(1-y) and equal to zero. At this condition we maximize the function and will get the maximum of the rumor spreading.

`(d(r(y)))/(dy)=2-4y=0`

Therefore we just need to find y:

`y=2/4=1/2`

So 1/2 or 50% of the population has heard the rumor when it is spreading fastest.

I hope it helps you!