?

AP® Calculus AB-BC

Free Version

Upgrade subject to access all content

Difficult

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

$40$ hrs

B

$20$ hrs

C

$3.214$ hrs

D

$1.607$ hrs