91Ó°ÊÓ

In Problems 31-42, find the population sizes for \(t=0,1\), 2, \(\ldots, 5\) for each recursion. Then write the equation for \(N_{t}\) as a function of \(t\). $$ N_{t+1}=2 N_{t} \text { with } N_{0}=3 $$

Find an expression for \(a_{n}\) on the basis of the values of \(a_{0}, a_{1}, a_{2}, \ldots\) \(-1,2,-3,4,-5, \ldots\)

In Problems , find the population sizes for \(t=0,1\), 2, \(\ldots, 5\) for each recursion. Then write the equation for \(N_{t}\) as a function of \(t\). $$ N_{t+1}=2 N_{t} \text { with } N_{0}=5 $$

Find an expression for \(a_{n}\) on the basis of the values of \(a_{0}, a_{1}, a_{2}, \ldots\) \(9,16,25,36,49\)

Find an expression for \(a_{n}\) on the basis of the values of \(a_{0}, a_{1}, a_{2}, \ldots\) \(5,7,9,11,13\)

Investigate the advantage of dimensionless variables. A population obeys the discrete logistic equation: $$ N_{t+1}=R_{0} \cdot N_{t}-b N_{t}^{2} $$ Find the possible fixed points of the population size (one fixed point will depend on the unknown parameters \(R_{0}\) and \(b\) ).

In Problems , find the population sizes for \(t=0,1\), 2, \(\ldots, 5\) for each recursion. Then write the equation for \(N_{t}\) as a function of \(t\). $$ N_{t+1}=3 N_{t} \text { with } N_{0}=2 $$

In Problems , find the population sizes for \(t=0,1\), 2, \(\ldots, 5\) for each recursion. Then write the equation for \(N_{t}\) as a function of \(t\). $$ N_{t+1}=3 N_{t} \text { with } N_{0}=7 $$

In Problems , find the population sizes for \(t=0,1\), 2, \(\ldots, 5\) for each recursion. Then write the equation for \(N_{t}\) as a function of \(t\). $$ N_{t+1}=5 N_{t} \text { with } N_{0}=1 $$

Find an expression for \(a_{n}\) on the basis of the values of \(a_{0}, a_{1}, a_{2}, \ldots\) \(2,0,2,0,2\)