Abacteria culture contains 300 cells initially and grows at a rate proportional to its size. after half an hour the population has increased to 540 cells. (a) write down the differential equation describing the situation. (b) solve the differential equation. (c) use the remaining information in the problem to solve for the two constants, and write down the model for the number of bacteria at time t. (d) how long until there are 1 bacteria