The Solution of the Equation $\frac { d P } { d t } = P ( 12 - 3 P )$

question 13

Multiple Choice

The solution of the equation $\frac { d P } { d t } = P ( 12 - 3 P )$ with initial condition $P ( 0 ) = 3$ is

• A) \(P = 12 / \left( 3 + e ^ { - 12 t } \right)\)
• B) \(P = 4 / \left( 3 + e ^ { - 12 t } \right)\)
• C) \(P = 4 / \left( 3 - e ^ { - 12 t } \right)\)
• D) \(P = 3 / \left( 12 + e ^ { - 12 t } \right)\)
• E) \(P = 3 / \left( 4 + e ^ { - 12 t } \right)\)

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Definitions:

SSE

Stands for Sum of Squared Errors, a measure of the variation or dispersion of data points around a regression line or mean.

SST

Often refers to the Total Sum of Squares, which is a measure used in statistical analysis to quantify the variation within a set of observations.

Linear Regression

A statistical method that models the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.

F Test

A statistical test used to determine whether there are significant differences between the variances of two or more groups.