A researcher is studying tumours in mice. The growth rate for the volume of the tumourV(t)

V(t)incm^3is given by dV/dt =1.45V(2ln(V+1)).

(a) Find all the equilibria and determine their stability using the stability condition.

(b) Draw the phase plot. On the plot identify each equilibrium as stable or unstable.

(c) Draw direction arrows for the case where the tumour starts at size3cm^ 3and for the case where the tumour starts at size9cm^3. Explain in biological terms what happens to the size of each of these tumours at time progresses

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