Doubling time is the length of time it takes for a quantity to double in size or value.

The number of bacteria in a liquid culture can be modelled as a continuous variable and grows at a rate proportional to the number of bacteria present. Initially, there are 5000 bacteria in the culture. After 3.5 hours there are a million bacteria.
a. What is the doubling time of the bacteria in the culture?
b. What assumption does the model make about the growth of the bacteria and how realistic is this assumption?