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.

Answer 1

"eventually means as t→∞
so, assuming k<0, that means a = 250000
So now you know that
250000(1 - e^k) = 250000/4
1-e^k = 1/4
e^k = 3/4
k = ln 3/4
N(t) = 250000(1 - e^(ln 3/4 * t))
...
But, since e^(ln 3/4) = 3/4, that gives
N(t) = 250000(1 - (3/4)^t)
so N has a (3/4)-life of 1 day

Answer 2

1243