A Ferocious Forest Fire

During a particularly hot summer, the area of a small forest was reduced by fire. The area, Akm2, of the surviving forest is modelled as being inversely proportional to t, the time in days since the start of the fire.

a) 5.5 days after the fire started, the area of the surviving forest was 2.6 km2. Find the constant of proportionality, k.

[2 marks]

b) Sketch the graph of A against t, stating the equations of any asymptotes.

[2 marks]

c) Suggest one reason why this model has the restriction t ≥ 1

[1 mark]

d) Suggest a refinement to this model that might make it more accurate

[1 mark]