525.sagews

Sage Tool 1

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

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

We define $K$, $M$, and $P_0$ below.

K=0.00009
M=1000
P_0=10

We assign $n$ and $\Delta$ (in place of $\Delta t$) and define the iteration procedure.

n=40
Delta=120/n
var('k')
t(k)=k*Delta
def P(k):
    list=[P_0]
    for i in range(1,k+1):
        list.append(list[i-1]+K*list[i-1]*(M-list[i-1])*Delta)
    return list
P(3)

[10, 12.6730000000000, 16.0513466691700, 20.3156459227746]

We carry out the iteration and assign its values to $t$ and $P$.

solution=[(t(k),P(n)[k]) for k in range(n)]

line(solution)

Now we plot the solution.