A simple model for population growth assumes that the growth rate of the population is proportional to the size of the population. If the size of the population at time t is p(t), then the growth rate, or rate of change of the population, is its derivative p’(t). So,
p’(t) = kp(t)
where k is the proportionality constant. Thus, p’(t) – kp(t) = 0 where p(t) = cekt is a basis for the solution space (c and k are constants determined from experimental data).

Question

A simple model for population growth assumes that the growth rate of the population is proportional to the size of the population. If the size of the population at time t is p(t), then the growth rate, or rate of change of the population, is its derivative p’(t). So,
p’(t) = kp(t)
where k is the proportionality constant. Thus, p’(t) – kp(t) = 0 where p(t) = cekt is a basis for the solution space (c and k are constants determined from experimental data).

anonymous · Answer

Case: The bacterium Escherichia coli (E. coli) is commonly found in the intestines of humans and other mammals. It poses severe health risks if it escapes into the environment. Under laboratory conditions, each cell of the bacterium divides itself into two for every 20 minutes. If we start with a single E. coli cell, how many will there by after 72 minutes?