The logistic model of growth takes the general form, y=k/1+be^-at where k, a and b are positive constants. (a) Find an expression for dy/dt and deduce that the gradient is positive. (b) Find an expression for d^2y/dt^2 and deduce that the graph is convex when t < (ln b)/a and concave when t > (ln b)/a. (c) State the coordinates of the point where the graph intercepts the y axis, and describe the behaviour of the graph as t ➜∞.

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.