(a) Use a graphing utility to graph the wolf population P(t) found in 45. (b) Use the

Chapter 2, Problem 46

(choose chapter or problem)

(a) Use a graphing utility to graph the wolf population P(t) found in Problem 45.

(b) Use the solution P(t) in Problem 45 to find \(\lim _{t \rightarrow \infty} P(t)\).

(c) Show that the differential equation in Problem 45 is a special case of Gompertz’s equation ((7) in Section 2.8).

When all the curves in a family \(G\left(x, y, c_{1}\right)=0\) intersect orthogonally all the curves in another family \(H\left(x, y, c_{2}\right)=0\), the families are said to be orthogonal trajectories of each other. See FIGURE 2.R.11. If \(d y / d x=f(x, y)\) is the differential equation of one family, then the differential equation for the orthogonal trajectories of this family is \(d y / d x=-1 / f(x, y)\). In Problems 47–50, find the differential equation of the given family. Find the orthogonal trajectories of this family. Use a graphing utility to graph both families on the same set of coordinate axes.