91Ó°ÊÓ

Investigate the behavior of the discrete logistic equation $$ x_{t+1}=r x_{t}\left(1-x_{t}\right) $$ Compute \(x_{t}\) for \(t=0,1,2, \ldots, 20\) for the given values of \(r\) and \(x_{0}\), and graph \(x_{t}\) as a function of \(t\). \(r=3.8, x_{0}=0.9\)

Investigate the behavior of the discrete logistic equation $$ x_{t+1}=r x_{t}\left(1-x_{t}\right) $$ Compute \(x_{t}\) for \(t=0,1,2, \ldots, 20\) for the given values of \(r\) and \(x_{0}\), and graph \(x_{t}\) as a function of \(t\). \(r=3.8, x_{0}=0\)

Write the first five terms of the sequence \(\left\\{a_{n}\right\\}\), \(n=0,1,2,3, \ldots\), and determine whether \(\lim _{n \rightarrow \infty} a_{n}\) exists. If the limit exists, find it. $$ a_{n}=\frac{n^{3}}{n+1} $$

In Problems , find the population sizes for \(t=0,1,2, \ldots, 5\) for each recursion. $$ N_{t+1}=\frac{1}{4} N_{t} \text { with } N_{0}=8192 $$

Write the first five terms of the sequence \(\left\\{a_{n}\right\\}\), \(n=0,1,2,3, \ldots\), and determine whether \(\lim _{n \rightarrow \infty} a_{n}\) exists. If the limit exists, find it. $$ a_{n}=\sqrt{n} $$

$$ \text { In Problems } \text { , write } N_{t} \text { as a function of } t \text { for each recursion } $$ $$ N_{t+1}=2 N_{t} \text { with } N_{0}=15 $$

Graph the Ricker's curve $$ N_{t+1}=N_{t} \exp \left[R\left(1-\frac{N_{t}}{K}\right)\right] $$ in the \(N_{t}-N_{t+1}\) plane for the given values of \(R\) and \(\bar{K} .\) Find the points of intersection of this graph with the line \(N_{t+1}=N_{t}\). R=3, K=15

$$ \text { In Problems } \text { , write } N_{t} \text { as a function of } t \text { for each recursion } $$ $$ N_{t+1}=2 N_{t} \text { with } N_{0}=7 $$

Write the first five terms of the sequence \(\left\\{a_{n}\right\\}\), \(n=0,1,2,3, \ldots\), and determine whether \(\lim _{n \rightarrow \infty} a_{n}\) exists. If the limit exists, find it. $$ a_{n}=n^{2} $$

Graph the Ricker's curve $$ N_{t+1}=N_{t} \exp \left[R\left(1-\frac{N_{t}}{K}\right)\right] $$ in the \(N_{t}-N_{t+1}\) plane for the given values of \(R\) and \(\bar{K} .\) Find the points of intersection of this graph with the line \(N_{t+1}=N_{t}\). R=2.5, K=12