Chapter 9, Problem 41P

Growth of many organisms can be modeled with the equation:

$\frac{dm}{dt}=k{m}^{3/4}\left[1-{\left(\frac{m}{m_{\max }}\right)}^{1/4}\right]$

where m(t) is the mass of the organism, m_maxis the assumed maximum mas, and k is a constant. Solve the equation for $0\le t\le 400$ days, given k=0.3 kg¹/4/day, m_max=300 kg and m(0)= 1 kg. Make a plot of m as a function of time.