# The Malthusian and Logistic Models of Population Growth

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.

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#### 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.

Your answer should be exact (it will contain logarithms)

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.