- #1
Jamin2112
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Homework Statement
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.
Homework Equations
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 = ee-rt+C
==> N = Kee-rt+C
Seems overly complicated. Is there some property of ln(ln(f)) that would help simplify? Suggestions, please.