Question

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

Modeling
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asked 2021-06-24
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?

Answers (1)

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]

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