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

question 34

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) \(f ( x ) = \frac { 20 } { 1 + 1.5 ^ { x } }\)

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