Suppose a population growth is modeled by the logistic equation $\frac { d P } { d t } = 0.0001 P ( 1000 - P )$ with P(0) = 10. Find the formula for the population after t years.
A) $P ( t ) = \frac { 1000 } { 1 + 99 e ^ { - 0.01 t } }$
B) $P ( t ) = \frac { 1000 } { 1 + 10 e ^ { - 0.01 t } }$
C) $P ( t ) = \frac { 1000 } { 1 + e ^ { - 0.01 t } }$
D) $P ( t ) = \frac { 100 } { 1 + 9 e ^ { - 0.01 t } }$
E) $P ( t ) = \frac { 1000 } { 1 + 9 e ^ { - 0.01 t } }$
F) $P ( t ) = \frac { 100 } { 1 - 99 e ^ { - 0.01 t } }$
G) $P ( t ) = \frac { 1000 } { 1 + 99 e ^ { - 0.1 t } }$
H) $P ( t ) = 1000 e ^ { 0.1 t }$

Question

Suppose a population growth is modeled by the logistic equation $\frac { d P } { d t } = 0.0001 P ( 1000 - P )$ with P(0) = 10. Find the formula for the population after t years.
A) $P ( t ) = \frac { 1000 } { 1 + 99 e ^ { - 0.01 t } }$ 
B) $P ( t ) = \frac { 1000 } { 1 + 10 e ^ { - 0.01 t } }$ 
C) $P ( t ) = \frac { 1000 } { 1 + e ^ { - 0.01 t } }$ 
D) $P ( t ) = \frac { 100 } { 1 + 9 e ^ { - 0.01 t } }$ 
E) $P ( t ) = \frac { 1000 } { 1 + 9 e ^ { - 0.01 t } }$ 
F) $P ( t ) = \frac { 100 } { 1 - 99 e ^ { - 0.01 t } }$ 
G) $P ( t ) = \frac { 1000 } { 1 + 99 e ^ { - 0.1 t } }$ 
H) $P ( t ) = 1000 e ^ { 0.1 t }$

Quizplus · Accepted Answer

The Answer is G

Suppose a Population Growth Is Modeled by the Logistic Equation dPdt=0.0001P(1000−P)\frac { d P } { d t } = 0.0001 P ( 1000 - P )dtdP​=0.0001P(1000−P)

Suppose a Population Growth Is Modeled by the Logistic Equation $\frac { d P } { d t } = 0.0001 P ( 1000 - P )$