Due to a stocking error 50 carp are added to a lake. The carp are prolific breeders with a population growth rate coefficient of 0.5 per month. Lake managers catch and remove K carp per month.  Let C(t) be the number of carp in the lake t months after their introduction. Explain why C(t) satisfies dC/dt=0.5C-K with C(0)=50.

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