Mathematica Tool 1

This Mathematica notebook is designed for  use with Activity 4 in Section 6.3

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 intial value problem with P(0)=10.

n=40;
Δ=120/n;
P=Range[n];

(Subscript[P, 0])=10;

P[[1]]=(Subscript[P, 0]);
For[i=2,i<n+1,i++,P[[i]]=N[P[[i-1]]+(k P[[i-1]] (M-P[[i-1]])) Δ]];
Solution=Partition[Riffle[(Range[n]-1) Δ,P],2];
Euler=ListPlot[Solution,PlotStyle->PointSize[0.01],PlotRange->{{0,120},{0,1200}}]

Here is our symbolic formula for P.

Pop[t_]:=((10000(E^(0.09 t)))/(990+10(E^(0.09 t))))
PopPlot=Plot[Pop[t],{t,0,120},PlotStyle->{Red,Thickness[0.01]}]
Show[Euler,PopPlot]