Under ideal conditions, a population of rabbits has an exponential growth rate of 11.6% per day. Consider an initial population of 400 rabbits. Find the exponential growth function.
A) $\mathrm { P } ( \mathrm { t } ) = 40 \mathrm { e } ^ { 0.116 \mathrm { t } }$
B) $P ( t ) = 100 \mathrm { e } ^ { 1.16 t }$
C) $\mathrm { P } ( \mathrm { t } ) = 400 \mathrm { e } ^ { 0.116 \mathrm { t } }$
D) $P ( t ) = 100 \mathrm { e } ^ { 11.6 \mathrm { t } }$

Question

Under ideal conditions, a population of rabbits has an exponential growth rate of 11.6% per day. Consider an initial population of 400 rabbits. Find the exponential growth function. 
A) $\mathrm { P } ( \mathrm { t } ) = 40 \mathrm { e } ^ { 0.116 \mathrm { t } }$
B) $P ( t ) = 100 \mathrm { e } ^ { 1.16 t }$
C) $\mathrm { P } ( \mathrm { t } ) = 400 \mathrm { e } ^ { 0.116 \mathrm { t } }$
D) $P ( t ) = 100 \mathrm { e } ^ { 11.6 \mathrm { t } }$

Quizplus · Accepted Answer

The exponential growth function is given by $P(t) = P_0 e^{rt}$, where $P_0$ is the initial population, $r$ is the growth rate, and $t$ is time. Given $P_0 = 400$ and $r = 0.116$, the correct function is $P(t) = 400 e^{0.116t}$.

Under Ideal Conditions, a Population of Rabbits Has an Exponential P(t)=40e0.116t\mathrm { P } ( \mathrm { t } ) = 40 \mathrm { e } ^ { 0.116 \mathrm { t } }P(t)=40e0.116t

Under Ideal Conditions, a Population of Rabbits Has an Exponential $\mathrm { P } ( \mathrm { t } ) = 40 \mathrm { e } ^ { 0.116 \mathrm { t } }$