Consider the growth of a population p(t). It starts out with p(0) = A. Suppose the growth is unchecked, and hence p = kp for some constant k. Then p(t) = Of course populations don't grow forever. Let's say there is a stable population size Q that p(t) approaches as time passes. Thus the speed at which the population is growing will approach zero as the population size approaches Q. One way to model this is via the differential equation p = kp(Q- p), p(0) = A. The solution of this initial value problem is p(t) = Hint: Proceed as in the last problem.

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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.