Between 1:00pm and 9:00pm, the population of a colony of bacteria de- creases exponentially. The population is 400,000 at 1:00pm and 250,000 at 5:00pm. (a) Describe the exponential decay. (b) Find a function P = f(t) that expresses the population in terms of time. Be sure to define t precisely. The choice is up to you. Include the domain. Explain your reasoning. 2 (c) Use your function to find the exact time when there are 200,000 bacteria. Do not use a calculator. (d) Use a calculator to approximate the clock time in part (c) to the nearest minute. (e) Find a function t = g(P) that expresses the time (as defined by you in poart (b) ) in terms of the population. State the domain of this function using set-builder notation