Math Problem Solver

Consider the logistic growth model, 𝑑𝑦/𝑑𝑡= 𝑟𝑦(𝑀 − 𝑦) where 𝑟 is the growth rate constant and 𝑀is

the carrying capacity. Find the expression of 𝑦. Consider that at 𝑡 = 0, 𝑦 = 𝑦0. Plot 𝑦 as a function of

𝑡 and characterize the nature of the curve. Prove that (a) when 𝑦 is small, 𝑦 grows exponentially and

(b) at 𝑦 → 𝑀, 𝑦 becomes constant.