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. [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 &alpha;=0.1&alpha;=0.1 and a carrying capacity of 10 million cells, how long does it take to reach &ldquo;detection&rdquo; stage at 5 million cells?

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