Maple Tool 1

This tool is designed for use with Activity 1 in Section 6.2.

Note that we use  rather than  for the proportionality constant. The lower case  is used as a counting index here.

We define  and  below, but the initial value  is defined farther down the page.

>	with(plots):

>	K:=0.00009; M:=1000;

>

We assign  and  (in place of ) and define the iteration procedure.

>	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:

Now we define the constant .

>

P(0):=10;

We carry out the iteration and assign the values to  and .

>	solution:=[seq([t(k),P(k)],k=0..n)]:

Now we plot the solution.

>	plot(solution, t=0..120, P=0..1000, style=line,symbol=circle, color=blue, thickness=2, xtickmarks=[20,40,60,80,100], ytickmarks=[200,400,600,800,1000]);

>