For this type of question, we have to establish an exponential function, which is usual for the growth of bacteria or population in general. In this exponential function, the time elapsed and the population will be related, and also from this equation will come the fact that when t=0 you only have the initial population.
Answer:
(a) and (b) If the population doubles each hour, and the initial population is 500, then we can set the following equation:
(c) From the above equation we get that when t=0 the number of bacteria is 500 which is the original population.