(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

As long as N isn't too small, the growth of cancerous tumors can be modeled by the Gompertz equation,

dN/dt = -rN*ln(N/K),

where N(t) is proportional to the number of cells in the tumor, and r,K>0 are parameters.

2. Relevant equations

3. The attempt at a solution

Separate out.

dN/[N*ln(N/K)]= -rdt

After much toil, I figured out that the left side is simply d/dN (ln(ln(N/K))

==> ln(ln(N/K)) = -rt + C

==> ln(N/K) = e^{-rt+C}

==> N/K = e^{e-rt+C}

==> N = Ke^{e-rt+C}

Seems overly complicated. Is there some property of ln(ln(f)) that would help simplify? Suggestions, please.

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# Homework Help: Another Messy Diffy Q

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