Suppose that a certain population satisfies the initial value problem dy/dt=r(t)y−k,y(0)=y0,dy/dt=rty−k,y0=y0, where the growth rate r(t) is given by r(t) = (1 + sin t)/5, and k represents the rate of predation. a. Suppose that k = 1/5. Plot y versus t for several values of y0 between 1/2 and 1. b.Estimate the critical initial population yc below which the population will become extinct.

Question

Suppose that a certain population satisfies the initial value problem

dy/dt=r(t)y−k,y(0)=y0,dy/dt=rty−k,y0=y0,

where the growth rate r(t) is given by r(t) = (1 + sin t)/5, and k represents the rate of predation.

a. Suppose that k = 1/5. Plot y versus t for several values of y0 between 1/2 and 1.

b.Estimate the critical initial population yc below which the population will become extinct.

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