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L.F. Richardson proposed a model to describe the spread of war fever. His proposal: If y(t) is the percent of the population advocating 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

Answer :

rodolforodriguezr

Answer:

y'(t)=ky(t)(100-y(t))

Step-by-step explanation:

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 k is the constant of proportionality

The differential equation that models the situation is given by:

[tex]y^{\prime} = ky(100 - y), k > 0[/tex]

What is the differential equation?

To build the differential equation, we consider that:

  • The rate of change is [tex]y^{\prime}[/tex].
  • The percentage of the population advocating war is y.
  • The percentage not advocating war is 100 - y.
  • In the multiplication, there is a positive constant of proportionality k.

Hence, the differential equation is:

[tex]y^{\prime} = ky(100 - y), k > 0[/tex]

More can be learned about differential equations at https://brainly.com/question/14423176

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