The function below represents the number of people who have a rumor t hours after it has started.

Question

N(t)=700/1+699e−0.4t.

(You may wish to sketch a graph of N(t) to help you understand this situation and answer the questions below.)

1) When is the rumor spreading fastest?
t=
I don't know how to solve this.

Answer 1

N(t) is the number of people
N'(t) is the rate of spread
N(t) = 700/(1 + 699e^(-0.4t))
N'(t) = 195720/(1 + 699e^(-0.4t))^2
We want the rate of spreading to be fastest. That is, when N'(t) is a maximum -- or when N"(t) = 0
Unfortunately,
N"(t) = 89,315,424 e^(0.4t)/(1 + 699e^(-0.4t))^3
this is just another exponential, so it is never zero. Is the problem maybe written wrong?

Answer 2

its all good I got it, I appreciate it. It was 5ln699/2