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Preliminary remarks

You may think of information as of a physical quantity which can be measured. In accordance with the Gallup Institute, information news diffuse through an adult population of fixed size P at a time rate proportional to the number of people who have not heard the news.

If N(t) is the number of people who have heard the news after t days, then
\begin{maplelatex} \begin{displaymath} \displaystyle\frac{dN}{dt} = k(P - N) \hspace*{3.5in}{(3)}\end{displaymath}\end{maplelatex}
The obvious fact that N(0) = 0 serves here as the initial condition, thus the solution of the initial value problem is given by
\begin{maplelatex} \begin{displaymath} N(t) = P(1 - e^{-kt}) \hspace*{3.5in}{(4)}\end{displaymath}\end{maplelatex}

Christine M Palmer
9/23/1998