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?

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

Step-by-step 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.

Therefore we just need to find y:

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

I hope it helps you!

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80