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# Let f(t) be the size of a paramecium population after t days. Suppose that y=f(t) satisfies the differential equation$y^{\prime}=.003 y(500-y), \quad y(0)=20 .$Describe this initial-value problem in words.

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If $f(t)$ is the size of a paramecium population after $t$ days, and it satisfies the initial-value problem

\begin{aligned} y'=.003(500-y), \quad y(0)=20, \end{aligned}

we can conclude that in the beginning, the size of a paramecium population was $20$. Then the size of a paramecium population after $t$ days is proportional to the difference between the number $500$ and the number $y=f(t)$ at the moment $t$ and it is increasing function.

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