Question

N(t) = 650/1+649 e^−0.5 t

(b) How many people will have heard the rumor after 4 hours?
After 9 hours?
(c) When will half the people have heard the rumor? t =

(d) When is the rumor spreading fastest? t =

Answer 1

Your problem doesn't state the original population, so you need to rephrase your homework question to give all the information.

You can use a program like Winplot to plot this function, and pick off the relevant data.

Answer 2

N(t) = 650 + 649e^-0.5t.

a. -0.5t = -0.5*4 = -2,
N(4) = 650 + 649 * e^-2,
= 650 + 649*0.1352,
= 650 + 87.8 = 737 people.

b. -0.5t = -0.5 * 9 = -4.5,
N(9) = 650 + 649*e^-4.5,
= 650 + 649 * 0.01111,
= 650 + 7.21 = 657 people.