Question

12 10 marks] Algae is growing in a fish tank. The biomass z(t) of the algae at time t is modelled by the Malthusian model dz dt = (b-d)2. Suppose that we buy a chemical that is intended to reduce the amount of algae. If the dosage of the chemical is p, then the birth and death rates of the algae are affected as follows: d(p)=2 and p) (a) On the same set of axes, sketch the graphs of the functions b(p) and d(p). Make a second sketch showing (5 marks) (b) Find conditions in terms of p for the extinction of the algae population. Hence conclude whether the (5 marks) the graph of r(p) b(p) -d(p chemical is suitable for its intended purpose.

Answer 1

p46 dep) b CP shown a3 in fig. 2. Th Alae Pohulain extinct if 2. p46 PP2sp46) 2.