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The Malthusian and Logistic Models of Population Growth

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Please see the attached file. This is one question but broken in parts.

Formula for Malthusian Model:
dP/dt = r*P

Formula for Logistic Model:
dP/dt=rP(1-P/K)

PS> I Prefer hand written work showing the steps if it is neat. It's up to you..I just have a hard time reading fractions & exponents in a word document etc.

(ie. (3/5)^2.

https://brainmass.com/math/basic-algebra/malthusian-logistic-models-population-growth-433124

Solution Preview

See the attached file.

Question:

Let P (t) represent a population of farm-raised catfish in a small lake at any
time t in days.

(a) If the population grows according to the Malthusian model, find the time for the
catfish population to triple if it grows by 10% in 45 days. Show all of you work.

According to the Malthusian model, we have
dP/dt = r*P
for some constant r. Separating variables we obtain
dP/P = r dt.
Integrating both sides we obtain
ln P(t) = rt + c
for some constant c. Exponentiating both sides we ...

Solution Summary

The solution solves problems involving catfish breeding assuming either the Malthusian model (unlimited exponential growth) or the more realistic logistic model of population growth.

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