Consider a generalized rabbit population model, as described in the textbook:{xn+1 = αxn+ βyn yn+1 = γαxn,
where xn is the number of the adult female rabbits in n-th generation, yn is the number of newborn female rabbits. Here α is the survival rate for the adult rabbits, β is the survival rate for the newborn rabbits, γ is the fertility parameter.

1. Is it possible that the population eventually dies out for some parameters α, β, γ? If ’yes’ describe all such parameters α, β, γ. Provide a Maple example.
2. Is it possible that we do not observe (numerically) either exponential growth or exponential decrease of the rabbit population with time? Explain this phenomenon with calculations. Provide a Maple example

6. A small lake is stocked with a certain species of fish. Use the simplified logistic model 4 P(t) = 1 to describe the population at time t > 0. The parameters A and k are positive constants. (b) After 4 years the population is 1500. What will the population be after 8 years? (Note that using the properties of the exponential function, you are expected to obtain an exact numerical answer, with no unevaluated exponentials or logarithms.)

11. A population of bacteria grows according to an exponential model. The initial size of the population is P, and 45 minutes later the population has grown to a size of 3P.. (a) Give an equation for the size P(t) of the population, after t seconds. Find all parameters involved.