Task 3 a) We are looking at a logistical growth model dN(t) _ w Y=guvm)=a-N(o-( M). N(0)=No>0: with internal growth rate a = 1/10 and bearing capacity M> 0. Describe in your own words how to determine the solution N (t). It is not necessary to explain every step of the bill, but the idea must be comprehensible (and it is permissible to use formulas if this simplifies the explanation). In the description, use II II II I! the words "separable , partial fraction splitting , initial condition" and "integration" (in the correct context). b) We consider a growth model that can be described with the scalar differential equation dP(t) T = f(P(t))s P(0) = Po 6 R, Pit) 2 0 with time t20 and (Df(P)=0.4-P (ii)f(P)=0.2-(300-PP"2) (iii)f(P)=0.6- (400P)-P- (P20) Which models contain which of the following features and why / why not? Write a paragraph in your own words for all the features (1) to (4). You can (but do not have to) use a P-f (P) coordinate system. Tip: You do not have to solve the differential equations. (1) If the initial population P o is zero, then there is no growth: P (t) 50 for all t20. (2) If the initial population P a is )ess than 50, the population dies out. (3} If the initial population P o is very large, then the population decreases in the beginning. (4) For any positive initial population P o > 0, P (t) approaches a finite value for t -) 0