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let's explore
the calculus.
The project of calculus.
HARVESTING OF INEXAUSTIBLE
NATURAL RESOURSES.
Mathematical part
Assumption
1. Let P(t) denote the size of a population at time t.
2. The model for exponentiel growth begins with
for some k>0 .
3. In this model the relative or specific, growth rate defined by
,Assume as a constant.
Calculation
In many cases,
is not constant but a function of P,Let
Suppose an environment is capable of substaining no more than a fixed
number K of individuals in its population .The quality is called the
carrying capacity of the environment
Special cases:
so now, without human intervation,we assume that the population
would behaves logistically ,then the logistic eqaution is,
where r > 0 is the intrinsic growth rate and K is the environment carring capacity.
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