Find the logistic function that satisfies the given conditions.
-Initial value $= 15$, limit to growth $= 60$, passing through $( 1,24 )$
A) $f ( x ) = \frac { 24 } { 1 + 2 ( 1 / 3 ) ^ { x } }$
B) $f ( x ) = \frac { 60 } { 1 + 3 ( 1 / 2 ) ^ { x } }$
C) $f ( x ) = \frac { 15 } { 1 + 3 ( 1 / 2 ) ^ { x } }$
D) $f ( x ) = \frac { 60 } { 1 + 2 ( 1 / 3 ) ^ { x } }$

Question

Quizplus · Accepted Answer

The general form of a logistic function is $f(x) = \frac{L}{1 + Ae^{-kx}}$, where $L$ is the limit to growth. Given $L = 60$ and the initial value $f(0) = 15$, we can substitute these values into the formula. The point $(1, 24)$ allows us to solve for $A$ and $k$. Among the options, only option B correctly represents a logistic function with these parameters, as it has the correct limit to growth (60) and satisfies the given point when the values are substituted.

Find the Logistic Function That Satisfies the Given Conditions =15= 15=15

Find the Logistic Function That Satisfies the Given Conditions $= 15$