A culture of bacteria in a laboratory satisfies the relation P=3t, where P (in thousands) is the population and t (in hours) is the time elapsed since the beginning of the experiment.
a. (a) Express t explicitly as a function of P in logarithmic form.
b. (b) Calculate, correct to two decimal places, the time required for the culture to reach P=5.
c. (c) For the function obtained in part (a), state its domain and range in the context of this situation and briefly justify your answer.