Sociologists sometimes use the phrase “socialdiffusion” to describe the way information spreads through a population.The information might be a rumor, a cultural fad, or news abouta technical innovation. In a sufficiently large population, the numberof people x who have the information is treated as a differentiablefunction of time t, and the rate of diffusion, dx/dt, is assumed tobe proportional to the number of people who have the informationtimes the number of people who do not. This leads to the equationdx/dt = kx(N - x),where N is the number of people in the population. Suppose t is in days, k = 1/250, and two people start a rumorat time t = 0 in a population of N = 1000 people. When will half the population have heard the rumor? (This is when the rumor will be spreading the fastest.)
Sociologists sometimes use the phrase “social
diffusion” to describe the way information spreads through a population.
The information might be a rumor, a cultural fad, or news about
a technical innovation. In a sufficiently large population, the number
of people x who have the information is treated as a differentiable
function of time t, and the rate of diffusion, dx/dt, is assumed to
be proportional to the number of people who have the information
times the number of people who do not. This leads to the equation
dx/dt = kx(N - x),
where N is the number of people in the population. Suppose t is in days, k = 1/250, and two people start a rumor
at time t = 0 in a population of N = 1000 people. When will half the population have heard the rumor? (This is
when the rumor will be spreading the fastest.)
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