Suppose that a particular pond can sustain up to 30,000 tilapia and that the undisturbed population of tilapia in this environment can be modeled according to the logistic model as dP/dt = 4(1 - P/30,000)P. Suppose that the farmer wishes to sell 15,000 fish per year. In this case, the harvest model will be constant. a. Following the constant harvest model, write an equation, involving a derivative, that governs the population of tilapia. b. What happens to the population if P = 5000? c. What happens to the population if P = 20,000? d. Find the two equilibria for this model.
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Suppose that a particular pond can sustain up to 30,000 tilapia and that the undisturbed population of tilapia in this environment can be modeled according to the logistic model as
dP/dt = 4(1 - P/30,000)P.
Suppose that the farmer wishes to sell 15,000 fish per year. In this case, the harvest model will be constant.
a. Following the constant harvest model, write an equation, involving a derivative, that governs the population of tilapia.
b. What happens to the population if P = 5000?
c. What happens to the population if P = 20,000?
d. Find the two equilibria for this model.
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