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

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. [T] The Gompertz equation has been used to model tumor growth in the human body. Starting from one tumor cell on day 1 and assuming $$α=0.1$$ and a carrying capacity of 10 million cells, how long does it take to reach “detection” stage at 5 million cells?

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Tasneem Almond

Octave code
syms P0 k t a.$$\displaystyle{P}={k}\cdot{\left({P}\frac{{0}}{{k}}\right)}^{{{e}^{{-{a}\cdot{t}}}}}.{v}{p}{a}{\left({s}{o}{l}{v}{e}{\left(\subset{s}{\left({P},{\left[{P}{0}{k}{a}\right]},{\left[{1}{10}^{{7}}{0.1}\right]}\right)}={5}\cdot{10}^{{6}},{t}\right)}\right)}$$
The result is
31.464555148849334319210049495334