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AP® Calculus AB-BC

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Moderate

Modeling Population Growth with Differential Equations

APCALC-JU8N0X

The growth rate of a population of ants is given by $\cfrac{dP}{dt} = k(200 – P)$, where $t$ is measured in days.

If the initial population of ants in an anthill is $20$, find the population as $t$ goes to infinity.

A

$20$

B

$ 100$

C

$ 200$

D

$ 180$