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Answer:
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!