Find the logistic function f with the given properties. $f ( 0 ) = 20$ , f has limiting value 500, and for small values of x, f is approximately exponential and doubles with every increase of 1 in x.
A) $f ( x ) = \frac { 500 } { 1 + 24 \left( 2 ^ { - x } \right) }$
B) $f ( x ) = \frac { 500 } { 1 + 24 \left( 1.5 ^ { - x } \right) }$
C) $f ( x ) = \frac { 500 } { 1 + 1.5 ^ { - x } }$
D) $f ( x ) = \frac { 1 } { 1 + 24 \left( 2 ^ { - x } \right) }$
E) $f ( x ) = \frac { 500 } { 1 + 2 ^ { - x } }$

Question

Find the logistic function f with the given properties. $f ( 0 ) = 20$ , f has limiting value 500, and for small values of x, f is approximately exponential and doubles with every increase of 1 in x.  
A) $f ( x ) = \frac { 500 } { 1 + 24 \left( 2 ^ { - x } \right) }$
B)   $f ( x ) = \frac { 500 } { 1 + 24 \left( 1.5 ^ { - x } \right) }$
C)   $f ( x ) = \frac { 500 } { 1 + 1.5 ^ { - x } }$  
D)   $f ( x ) = \frac { 1 } { 1 + 24 \left( 2 ^ { - x } \right) }$  
E)   $f ( x ) = \frac { 500 } { 1 + 2 ^ { - x } }$

Quizplus · Accepted Answer

The correct logistic function is $f(x) = \frac{500}{1 + 24(2^{-x})}$ because it satisfies all given conditions: $f(0) = 20$, the limiting value is 500, and it doubles for every increase of 1 in x, which is represented by the $2^{-x}$ term in the denominator.

Find the Logistic Function F with the Given Properties f(0)=20f ( 0 ) = 20f(0)=20

Find the Logistic Function F with the Given Properties $f ( 0 ) = 20$