Question 3 (10 marks). The concentration of antibiotic in the bloodstream t hours after

being injected is given by the function

C(t) = [tex]\frac{2t^{2} + t }{t^{3} + 50}[/tex]

where C is measured in milligrams per liter of blood.

a. Find the rate of change of C(t).

b. Determine the rate of change for t = 8, 12, 24, and 36.

c. Briefly describe what seems to be occurring as the number of hours increases.