Logistic Equation For the logistic IVP, we derived a solution formula (10) from the implic...

Logistic Equation For the logistic IVP, we derived a solution formula (10) from the implicit solution (7) for the case of 0 < y0 < L.

(a) Show that the same solution formula (10) results from (7) if y0 > L.

(b) Show that if y0 = L, the solution must be derived from the DE (6), but that coincidentally the formula (10) also gives the correct answer.

(c) For each of the three cases 0 < y0 < L, y0 = L, and y0 > L, show how the solution formula (10) predicts the qualitative behavior of the solutions, shown in Fig. 8.

(d) Show that for 0 < y0 < L, the inflection point of the logistic curve (10) occurs at y(t) = L/2, where t has the value

.

What is the rate of change at t*?