In a Newly Made Preserve in a Zoo, 400 Rabbits $\frac { d R } { d t } = 8 R \left( 1 - \frac { R } { 400 } \right) , R ( 0 ) = 6,000$

Multiple Choice

In a newly made preserve in a zoo, 400 rabbits were released. The monthly maximum population growth rate is 8%. Population ecologists have determined that the forest preserve can sustain a population of 6,000 rabbits, and the population will follow a logistic growth model. Which of the following is a logistic differential equation that models the rabbit population, R(t) ?

A) $\frac { d R } { d t } = 8 R \left( 1 - \frac { R } { 400 } \right) , R ( 0 ) = 6,000$
B) $\frac { d R } { d t } = 0.08 R \left( 1 - \frac { R } { 6,000 } \right) , R ( 0 ) = 400$
C) $\frac { d R } { d t } = 0.08 R \left( 1 - \frac { R } { 400 } \right) , R ( 0 ) = 6,000$
D) $\frac { d R } { d t } = 0.08 \left( 1 - \frac { R } { 6,000 } \right) , R ( 0 ) = 400$
E) $\frac { d R } { d t } = 0.08 \left( 1 - \frac { R } { 6,000 } \right) , R ( 0 ) = 400$ .