Population Calculus Problem

Question

The number, N, of people who have heard a rumor spread by mass media at time, t , is given by

N(t) = a(1 - e^(kt))

There are 250000 people in the population who hear the rumor eventually. 25 percent of them heard it on the first day. Find a and k , assuming t is measured in days.

a = ?

k = ?

Answer 1

There are 250000 people in the population who hear the rumor eventually.

It means that a = 250000

25 percent of them heard it on the first day.

It means that 1 - e^k = 0.25

Solving for k as follows

e^k = 0.75

k = ln (0.75) = -0.29

I should mention here that k is usually positive, because the exponent is usually written as exp (-kt). Omitting the minus resulted in k being negative.