[0, 50] and P
[0, 1000]. Show the solution trajectories that have
the initial conditions P(0) = 50,
100, 200,
and 400. Briefly describe the shape of
the solution curves and their relation to the slope field.1. a. The Malthusian growth model is given by
Suppose that r = 0.017 and
P0 = 100. Find the
solution for this model and determine the doubling time. Use Maple's
DEplot function to graph the slope field for this model for
t
[0, 50] and P
[0, 1000]. Show the solution trajectories that have
the initial conditions P(0) = 50,
100, 200,
and 400. Briefly describe the shape of
the solution curves and their relation to the slope field.
b. Consider the logistic growth model given by
where is r as before and M = 800. If P0 = 100, then find the solution of this differential equation (using Maple). How long until this solution doubles? How much longer until it reaches 400?
c. Use Maple's DEplot function to graph the slope field for this
logistic growth model for t
[0, 200] and P
[0, 1000]. Show the solution trajectories that have
the initial conditions P(0) = 50,
100, 200,
400, 800,
and 1000. Briefly describe the shape of
the solution curves and their relation to the slope field.