Question

The following question consider the Gompertz equation, a modification for logistic growth, which is often used for modeling cancer growth, specificall

Modeling
The following question consider the Gompertz equation, a modification for logistic growth, which is often used for modeling cancer growth, specifically the number of tumor cells. Assume that for a population K=1000 and α=0.05.. Draw the directional field associated with this differential equation and draw a few solutions. What is the behavior of the population?

2021-06-25

Samples of the solutions::
Octave or Matlab code
i=1; figure;hold on;
while i<5
$$\displaystyle{P}{0}={10}^{{i}}$$;
t=linspace(0,100,100000)';
$$\displaystyle{\left[{t},{P}\right]}={o}{d}{e}{45}{\left(\circ{\left({t},{P}\right)}{0.05}\cdot{P}.\cdot{\log{{\left({1000}\frac{.}{{P}}\right)}}},{t},{P}{0}\right)}$$;
plot(t,P);
i=i+1;
endwhile;
legend$$("P_0=10","P_0=100","P_0=1000","P_0=10000")$$;
[Graph]