Find the logistic equation that satisfies the following differential equation and initial condition.
$\frac { d y } { d t } = 3.4 y \left( 1 - \frac { y } { 53 } \right) , y ( 0 ) = 13$
A)
$$y = \frac { 53 } { 1 + \frac { 40 } { 13 } e ^ { - 3.4 t } }$$
B)
$$y = \frac { 53 } { 1 + \frac { 40 } { 13 } e ^ { 3.4 t } }$$
C)
$$y = \frac { 53 } { 1 + \frac { 66 } { 13 } e ^ { - 3.4 t } }$$
D)
$$y = \frac { 53 } { 1 + \frac { 66 } { 13 } e ^ { 3.4 t } }$$
E) none of the above

Question

Quizplus · Accepted Answer

The given differential equation is a logistic growth equation with a carrying capacity of 53 and a growth rate of 3.4. The initial condition $y(0) = 13$ allows us to solve for the constant in the logistic equation. The correct logistic equation that satisfies both the differential equation and the initial condition is option A, as it correctly incorporates the carrying capacity, growth rate, and initial condition into the logistic model formula.

Find the Logistic Equation That Satisfies the Following Differential Equation dydt=3.4y(1−y53),y(0)=13\frac { d y } { d t } = 3.4 y \left( 1 - \frac { y } { 53 } \right) , y ( 0 ) = 13dtdy​=3.4y(1−53y​),y(0)=13

Find the Logistic Equation That Satisfies the Following Differential Equation $\frac { d y } { d t } = 3.4 y \left( 1 - \frac { y } { 53 } \right) , y ( 0 ) = 13$