A Colony Of Bacteria Is Growing In A Petri Dish Which Has A Maximum Ca A Colony Of Bacteria Is Growing In A Petri Dish Which Has A Maximum Ca A colony of bacteria is growing in a petri dish which has a maximum capacity of 140mg. The mass of bacteria is increasing at a rate given by the logistic equation. Initially, there is 2mg of bacteria and the rate of increase is 1mg per day. The general form of the logistic differential equation is given as y' = k * y * (1 - y/M) where y(t) is the mass of bacteria at time t, M is the maximum capacity (140 mg), and k is a constant to be determined. Given the initial conditions y(0) = 2 mg, and the initial rate y'(0) = 1 mg/day, we can find k and then write the explicit equation for the rate of change of mass.
Paper For Above instruction The logistic growth model is a classical mathematical representation used to describe populations or quantities that grow rapidly at first but slow as they approach a maximum carrying capacity. It is widely applied in biological studies, including bacterial growth, as it realistically portrays the limited resources and environmental constraints impacting growth dynamics. In this context, the differential equation governing bacterial mass y(t) is given by: y' = k * y * (1 - y / 140) where y(t) is in milligrams (mg) at time t (days), M = 140 mg represents the maximum capacity, and k is the growth rate constant to be determined based on initial conditions. Determining the value of k At t = 0, the initial mass y(0) = 2 mg, and the rate of increase y'(0) = 1 mg/day. Substituting into the differential equation: 1 = k * 2 * (1 - 2/140) Calculating the term in parentheses: 1 - 2/140 = 1 - 1/70 = 69/70