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How many trout were in the lake when the carp were introduced?

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When will the populaiton of trout be zero?

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Sketch the number of trout as a funciton of time.

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When is the rate of increase of carp equal to the rate of decrease of trout?

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When is the number of carp equal to the number of trout?

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Trout and carp are types of fish. A lake contains a number of trout. At a certain time, \\var{a} carp are introduced into the lake and start eating the trout. As a consequence, the number of trout, $N$, decreases according to \\[N=\\var{b}-e^{\\var{c}t}\\] where $t$ is the time in months after the carp are introduced.

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The population of carp, $P$, increases according to \\[\\frac{dP}{dt}=\\var{d}P\\]

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