Once activated, a population of self-replicating nano-bots is known to triple every four hours. Suppose that there are initially 50 nano-bots.

(a) What is the size of the population after 12 hours?

(b) Use an exponential function C(t) = C0e^rt to represent the population after t hours, and solve for C0 and r.

(c) Estimate the size of the population after 33 hours. Your answer should be given in the most exact representation (i.e., not a decimal).