At a time denoted as t = 0, a technological innovation is introduced to 20 out o

Question

At a time denoted as t = 0, a technological innovation is introduced to 20 out of a community, of 1 000 people. After 30 days, 45 people have the innovation. Assume that the speed at which the innovation is adopted by the population is directly proportional to the number interaction between those who have the innovation and those that do not have it. Write a differential equation which models the number y of people with innovation after t days. Make sure to include the initial conditions Rewrite the differential equation as a Bernoulli differential equation. Solve it as a Bernoulli differential equation using the correct substitution.

Explanation / Answer

(a) dx/dt=kx log x= kt+c at t=0 x=20 at t=30 x=45 c=log 20=2.995=3 k=0.027 diff. eq. is dx/dt=0.027 t (b) dx/dt=0.027 t (c) solution is written above we will get log x= 0.027t+3 x=e^(0.027t+3) x=20e^0.027t

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