1. Consider the following model that mimics in a simplistic way the biological growth process of a particular living species: dy dt = 1 - 2y Here y is the biomass of the species. (a) Solve the differential equation by separation of variables. (b) In addition, solve the differential equation by a simple change of variables by setting z(t) = 1 - 2y(t) and translating this to a differential equation in terms of the variable z(t). (c) Determine the species equilibrium level, by setting dy/dt = 0. Also give proper details that explain how you can determine the equilibrium from your solution for y(t) in (b) above. (d) Is the equilibrium locally stable and why, or why not? A simple intuitive argument is all that is needed here. Comment on the biological implications. (e) Provide a rough sketch of the solution of the equation for several initial conditions. On the same axis plot the equilibrium. [10 marks]