Maple Tool1.mws

Section 6.3

Maple Tool 1

This Maple file is designed to be used with Activity 4 in Section 6.3.

>    with(plots):with(DEtools):

Here are the values of K  and M  .

>    K:=0.00009;
M:=1000;

Here is the Euler's Method approximation to the solution of the initial value problem with P(0) = 10 .

>    n:=40;
Delta:=120/n;
t:=k->k*Delta;
P := proc(k)

>         P(k) := P(k-1)+K*P(k-1)*(M-P(k-1))*Delta;

>    end:
 P(0):=10;
solution:=[seq([t(k),P(k)],k=0..n)]:
Euler:=plot(solution, t=0..120, P=0..1000, style=point,color=blue, symbol=circle, xtickmarks=[20,40,60,80,100], ytickmarks=[200,400,600,800,1000]):%;

>   

Here is our symbolic formula for P .

>    Pop:=t->10000*exp(0.09*t)/(990+10*exp(0.09*t));

>    PopPlot:=plot(Pop(t),t=0..120, thickness=2, xtickmarks=[20,40,60,80,100], ytickmarks=[200,400,600,800,1000]):%;

>    display(Euler, PopPlot);

>   

>