L.F. Richardson proposed a model to describe the spread of war fever. His proposal: If y(t) is the percent of the population adv
ocating war at time t, then the rate of change of y(t) at any time is proportional to the product of the percentage of the population advocating war and the percentage not advocating war. Set up a differential equation that is satisfied by y(t). (Note: Use k for the constant of proportionality with k > 0.)y' = ____________ , k > 0
The rate of change of y(t) at any time is the derivative of y with respect to time y, y'(t)
If y(t) is the percent of the population advocating war at time t
then 100-y(t) is the percent of the population not advocating war
The product of the percentage of the population advocating war and the percentage not advocating war would be
y(t)(100-y(t))
If the rate of change of y(t) at any time is proportional to the product of the percentage of the population advocating war and the percentage not advocating war, then
y'(t)=ky(t)(100-y(t))
where <em>k is the constant of proportionality
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