If the number of bacteria in a culture grows from 20,000 to 60,000 in 2 hours, then the growth constant is

A) $\frac { 3 } { \ln 2 }$
B) $\frac { 2 } { \ln 3 }$
C) $\frac { \ln 2 } { 3 }$
D) $3 \ln 2$
E) $\frac { \ln 3 } { 2 }$

Question

If the number of bacteria in a culture grows from 20,000 to 60,000 in 2 hours, then the growth constant is

A) $\frac { 3 } { \ln 2 }$
B) $\frac { 2 } { \ln 3 }$
C) $\frac { \ln 2 } { 3 }$
D) $3 \ln 2$
E) $\frac { \ln 3 } { 2 }$

Quizplus · Accepted Answer

The growth of bacteria can be modeled by the exponential growth equation $N = N_0e^{kt}$, where $N$ is the final amount, $N_0$ is the initial amount, $k$ is the growth constant, and $t$ is time. Given $N_0 = 20,000$, $N = 60,000$, and $t = 2$ hours, we can solve for $k$. Rearranging the equation gives $k = \frac{\ln(N/N_0)}{t} = \frac{\ln(60,000/20,000)}{2} = \frac{\ln(3)}{2}$.

If the Number of Bacteria in a Culture Grows from 20,000