Find the Logistic Function F with the Given Properties $f ( 0 ) = 1$

Multiple Choice

Find the logistic function f with the given properties. $f ( 0 ) = 1$ , f has limiting value 20, and for small values of x, f is approximately exponential and grows by 50% with every increase of 1 in x.

A) $f ( x ) = \frac { 1 } { 1 + 1.5 ^ { - x } }$
B) $f ( x ) = \frac { 20 } { 1 + 19 \left( 1.5 ^ { - x } \right) }$
C) $f ( x ) = \frac { 20 } { 1 + 2 ^ { - x } }$
D) $f ( x ) = \frac { 20 } { 1 + 19 \left( 2 ^ { - x } \right) }$
E) $f ( x ) = \frac { 20 } { 1 + 1.5 ^ { x } }$