Respuesta :
Answer:
a. The population does not become extinct in finite time.
Step-by-step explanation:
The model for the population of the fishery is
[tex]dP/dt = P(a-bP)-h, P(0) = P_0[/tex]
If we rearrange and replace the constants we have:
[tex]\frac{dP}{P(7-P)-49/4} =dt\\\\-4 (\frac{dP}{4(P-7)P+49}) =dt\\\\-4 \frac{dP}{(2P-7)^2} =dt\\\\-4 \int\frac{dP}{(2P-7)^2} =\int dt\\\\-4(-\frac{1}{2(2P-7)})=t+C\\\\\frac{2}{2P-7}=t+C\\\\ t=0 \,\,\, P(0)=P_0\\\\\frac{2}{2P_0-7}=0+C\\\\C=\frac{2}{2P_0-7}[/tex]
Now we can calculate if the population become 0 in any finite time
[tex]\frac{2}{2P-7}=t+\frac{2}{2P_0-7}\\\\\frac{2}{2*0-7}=t+\frac{2}{2P_0-7}\\\\-\frac{2}{7}=t+\frac{2}{2P_0-7}\\\\[/tex]
To be a finite time, t>0
[tex]t=-\frac{2}{7}-\frac{2}{2P_0-7}=0\\\\-\frac{2}{2P_0-7}=\frac{2}{7}\\\\7-2P_0=7\\\\P_0=0[/tex]
We can conclude that the only finite time in which P=0 is when the initial population is 0.
Because P0 is a positive constant, we can say that the population does not become extint in finite time.
As per the model of the harvesting the uses both the qualitative and the quantitative analytical methods. Hence the answer is option A that is the population does not get extinct in finite time.
Determine the population that gets extinct in a finite time.
The model of a constant number H and the fishes of the harvest from a the fishery per unit if time then the popualtion of the model is given as P(t). The model shows the dP/dt = P(a − bP) − h, P(0) = P0 relation
The aspects of the model can be shown by the above-given relations dP/dt = P(a − bP) − h, P(0) = P0, here a, b, h, and P0 are the positive constants. and taking a = 7, b = 1, and h = 49 4. Hence the model states that the popualtion does will not determine the population and will not get extinct in finite time.
Find out more information about the harvesting model.
brainly.com/question/24343041
