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).