Modelling Population Growth?

📌 CONCEPT: The population growth can be modelled using the logistic differential equation, which describes how the rate of change of the population is proportional to the product of the current population and the time elapsed.

📐 RULE / FORMULA: The logistic differential equation is given by dP/dt = kP(t), where P(t) is the population at time t and k is the growth rate constant.

💡 WORKED EXAMPLE: Given the initial population P(0) = 5000 and after 2 years P(2) = 7000, we need to find the time when the population will double. Let's assume P(t) = P0 * e^(kt), where P0 is the initial population. Using the given values, we can solve for k and then find the time when P(t) = 2*5000.

⚠️ COMMON MISTAKE: Students often confuse the logistic differential equation with the exponential growth equation and fail to take into account the initial population and the time elapsed in the model.