Doubling time is an intuitive measure of the rate of growth of a system. For example, it is especially useful for the initial period of growth of a population when growth rate only depends on the number of individuals and not any external pressures such as resource scarcity. Assume that a population grows by a fraction q each year. Given an initial population of P, the current population C at time 1 (measured in years) is then C(1) = P + qP = P (1 + q) .

Similarly, C(2) = C(1) (1 + q) = P (1 + q)

2

.

The pattern should be clear now. In general, after t years we have C(t) = P (1 + q)

t

.

Calculate the doubling time, td, as a function of q.

Typical doubling times are

a. About 29 hours for human cardiac stem cells.

b. About 15 hours for Escherichia coli in the human gut.

c. About 20 minutes for Escherichia coli in the laboratory.

d. About 25 hours for Salmonella enterica in the human gut.

e. A rat population can double in size in around 7 weeks.