Suppose a Population Growth Is Modeled by the Logistic Equation $\frac { d P } { d t } = 0.01 P - 0.0001 P ^ { 2 }$

Multiple Choice

Suppose a population growth is modeled by the logistic equation $\frac { d P } { d t } = 0.01 P - 0.0001 P ^ { 2 }$ with P(0) = 10. Find the formula for the population after t years.

A) $P ( t ) = \frac { 100 } { 1 + 9 e ^ { - 0.01 t } }$
B) $P ( t ) = \frac { 100 } { 1 + 10 e ^ { - 0.01 t } }$
C) $P ( t ) = \frac { 100 } { 1 + e ^ { - 0.01 t } }$
D) $P ( t ) = \frac { 10 } { 1 + 9 e ^ { - 0.01 t } }$
E) $P ( t ) = \frac { 10 } { 1 + e ^ { - 0.01 t } }$
F) $P ( t ) = \frac { 100 } { 1 - 9 e ^ { - 0.01 t } }$
G) $P ( t ) = \frac { 100 } { 1 + 9 e ^ { - 0.1 t } }$
H) $P ( t ) = 100 e ^ { 0.01 t }$