Given the demand and supply function of x between 2010 and 2025 is estimated to be;

D(t) = 0.005t² + 0.15t + 2 (0 < t < 15)

S(t) = - 0.01t² + 0.25t + 1 (0 < t < 15)

Where D(t) and S(t) are measured in million and t = 0 corresponds to the year 2010.

a) If A(t) is the gap between the demand and supply of x over the period in question. Find the function of A(t). (2 marks)

b) Find the interval where the function A(t) is decreasing and where it is increasing. Interpret your result. (4 marks)

c) Find the relative extreme of A. (2 marks)