Answer Happy

Question 2 In this question, we continue to explore the extremes of the model in Question 1. (a) Show that limy[1-y] =-y logy. You should treat y> 0 as a constant when computing this limit. Hint: Use a - e log a Your calculation shows that the ODE (1) discussed in Question 1 reduces to dy(t) dt = -Ay(t) log y(t) (where y(t) > 0) (**) upon taking the limit a → 0+. This can be thought of as an extreme asymmetric limit of the original differential equation where ymax is shifted to the value 1/e. (Just to be clear, there is no need for you to show this but you might be interested in checking this on your own nevertheless.) (b) Find the general solution to the differential equation (**). In the final two parts, assume that A = 1. (c) Determine the solution corresponding to the initial condition y(0) = 31. (d) Discuss the value of the limit lim y(t) for the solution you have found. t→∞