AP® Calculus AB-BC

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Differential Equation with Population Growth

APCALC-RZFJAQ

Population $y$ grows according to the equation $\cfrac { dy }{ dt } =ky$, where $k$ is a constant and $t$ is measured in years.

If the population doubles every $6$ years, then the value of $k$ is

A

$\ln { 2 } $

B

$\cfrac { \ln { 2 } }{ 2 } $

C

$\ln { \cfrac { 1 }{ 2 } } $

D

$\cfrac { \ln { 2 } }{ 6 } $