AP® Calculus AB-BC

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Bacteria Growth

APCALC-XMM4R8

The growth of a bacterial culture is modeled by the logistics equation:

$$y=\frac { 40 }{ 1+39{ e }^{ -1.14t } } $$

...where $y$ represents the number of grams of bacteria present after time $t$ hours.

At what time is the amount of bacteria increasing most rapidly?

A

$40\text{ hrs}$

B

$20\text{ hrs}$

C

$3.214\text{ hrs}$

D

$1.607\text{ hrs}$