The logistic model for population growth developed by P.F. Verhulst, is given by dp = ap – bp, dt p(0) = P, > 0 where p = p(t) is the population at time t and a, b are positive constants. Show that p(t) = ар. and explain why Po # 0, (a) bp, + (a – bp, )e at ª . (b) Find the limit of p(1) when (i) (ii) t →-00.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.