The subject is Differential Equations. Please label the final answers. Thanks. T

Question

The subject is Differential Equations. Please label the final answers. Thanks. The subject is Differential Equations. Please label the final answers. Thanks. oo T-Mobile LTE 8:28 AM '? 7696. a urses1.webwork.maa.or (1 point) Suppose that a population develops according to the logistic equation dP = 0.1P-0·00025P2 dt where t is measured in weeks. (a) What is the carrying capacity? (b) Is the solution increasing or decreasing when P is between 0 and the carriying capacity? (c) Is the solution increasing or decreasing when P is greater than the carrying capacity? increasing decreasing

Explanation / Answer

dP/dt = 0.1P - 0.00025P2

The carrying capacity of a biological species in an environment is the maximum population size of the species that the environment can sustain indefinitely.

so, dP/dt = 0 for maximum carrying capacity

0.1P - 0.00025P2 = 0

0.1 P =  0.00025P2

P = 400

(ii) Solution is increasing in between 0 to carrying capacity. As, maximum capacity would be at 400 so first population will increase and then it will be reduced.

(iii) Solution will be decreasing in between carrying capacity to further. As , maximum capacity would be at 400 so population will decrease after reacing carrying capacity.

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