The population of a strain of bacteria in a nutrient solution doubles every 3 hours. Initially, at time t=0, the culture contains 1.5×106 bacteria.
a. (i) Form an exponential function P(t) that models the population (number of bacteria) after t hours, restricting the domain to biologically meaningful values.
b. (ii) Using the model, calculate the population after 9 hours.
c. (iii) Determine the least time (to the nearest tenth of an hour) required for the population to reach 2.4×107. State whether the answer obtained lies within the chosen domain and comment briefly.