Match the logistic differential equation and initial condition with the graph of its solution shown below.
A) $\frac { d y } { d t } = y \left( y - \frac { 1 } { 15 } \right) , ( 0,8 )$
B) $\frac { d y } { d t } = y \left( y - \frac { 1 } { 15 } \right) , ( 0,12 )$
C) $\frac { d y } { d t } = y \left( y - \frac { 1 } { 15 } \right) , ( 0,6 )$
D) $\frac { d y } { d t } = y \left( y - \frac { 1 } { 15 } \right) , ( 0,15 )$
E) $\frac { d y } { d t } = y \left( y - \frac { 1 } { 8 } \right) , ( 0,15 )$

Question

Match the logistic differential equation and initial condition with the graph of its solution shown below. 
A) $\frac { d y } { d t } = y \left( y - \frac { 1 } { 15 } \right) , ( 0,8 )$ 
B) $\frac { d y } { d t } = y \left( y - \frac { 1 } { 15 } \right) , ( 0,12 )$ 
C) $\frac { d y } { d t } = y \left( y - \frac { 1 } { 15 } \right) , ( 0,6 )$ 
D) $\frac { d y } { d t } = y \left( y - \frac { 1 } { 15 } \right) , ( 0,15 )$ 
E) $\frac { d y } { d t } = y \left( y - \frac { 1 } { 8 } \right) , ( 0,15 )$

Quizplus · Accepted Answer

The solution graph approaches a stable equilibrium at y=1/15, which is what the logistic equation with initial condition (0,8) predicts.

Match the Logistic Differential Equation and Initial Condition with the Graph