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)).

Question

There are 450000 people in the population who hear the rumor eventually. 14 percent of them heard it on the first day. Find a and k , assuming t is measured in days.

Answer 1

as t ---> infinity , N --->a = 450,000
.14 * 450,000 = 63,000 when t = 1
so
63,000 = 450,000 [ 1 - e^-k ]
0.14 = 1 - e^-k
e^-k = 1 - .14 = 0.86
ln e^-k = -k = ln 0.86 = -0.151
k = 0.151