Chapter 8.1, Problem 86E

(a)

To determine

The table $N_j$ for first 20 terms to the nearest integer, if $N_{j+1}=\left[\frac{2}{1+\left(N_j/K\right)}\right]N_j$, $N_1=230$ and $K=5000$.

(b)

To determine

The graph of sequence $N_j$ for $j=1,2,3,\mathrm{...},20$.

(c)

To determine

The interpretation of the growth of bacteria when the nutrients are limited.

(d)

To determine

The conjecture about $K$ and check the conjecture by changing the value of $K$ in the formula of Verhulst’s model.