Question

in this exercise you are asked to approximate the growth of the world population using the logistic differential equation:

Answer 1

From the logistic population differential equation for approximate the growth of the world population , which is given here as $P = L/1+ e^{-k(x-x_{0} )$

The general form of the logistic population equation is given as $dP/dt = kP(1- P/L)$. While k is the relative growth rate, L is the carrying capacity.An ordinary differential equation with a logistic function as the solution is known as a logistic differential equation. Standard exponential functions do not account for the limitations that prevent infinite growth, but logistic functions correct this oversight. This is how bounded growth is represented by logistic functions. These contexts include machine learning, chess ratings, medical therapy (e.g., modelling tumour growth), economics, and even language adoption research.

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