Find the logistic function that satisfies the given conditions.
-Initial population $= 6$, maximum sustainable population $= 18$, passing through $( 1,13 )$
A) $f ( x ) = \frac { 6 } { 1 + 2 ( 0.44 ) ^ { x } }$
B) $f ( x ) = \frac { 6 } { 1 + 2 ( 0.12 ) ^ { x } }$
C) $f ( x ) = \frac { 18 } { 1 + 2 ( 0.11 ) ^ { x } }$
D) $f ( x ) = \frac { 18 } { 1 + 2 ( 0.22 ) ^ { x } }$

Question

Quizplus · Accepted Answer

The logistic function is given by $ f(x) = \frac{L}{1 + be^{-kx}} $. Here, $ L = 18 $ and initial population is 6, so $ b = \frac{L - P_0}{P_0} = 2 $. The function passes through (1,13), which helps determine $ k $. Solving gives $ f(x) = \frac{18}{1 + 2(0.22)^x} $.

Find the Logistic Function That Satisfies the Given Conditions =6= 6=6

Find the Logistic Function That Satisfies the Given Conditions $= 6$