The population of walleye pike in a large lake is given by the differential equation
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where P(t) is the number of fish, in thousands, in the lake after t days and H is a daily harvesting rate.

III. Finally assume H(t) = {0.5 t < 30}
{ 0 t 30}

Investigate the behavior of the fish population in this case. In particular, discuss such questions as

i) For what initial population sizes will the population eventually die out?

ii) For what initial population sizes, if any, will the population eventually reach equilibrium?

Give, analytically, all equilibrium points and classify as stable, unstable, semistable.