Find the logistic function f with the given properties. HINT [See Example 1.]
f has limiting value 7 and passes through (0, 1) and (1, 2).
Solution
general form of logistic equation is f(x) =N/(1+ae-bx), where N is limiting value snd a,b are
constants
f has limiting value 7
f(x) =7/(1+ae-bx)
passes through (0, 1)
1=7/(1+ae0)
1=7/(1+a)
1+a=7
a=6
f(x) =7/(1+6e-bx)
passes through (1, 2).
2 =7/(1+6e-b)
(1+6e-b)=7/2
6e-b=5/2
e-b=5/12
eb=12/5
b=ln(12/5)
f(x) =7/(1+6e-(ln(12/5))x) is the logistic function.
Find the logistic function f with the given properties. HINT [See Ex.pdf
1. Find the logistic function f with the given properties. HINT [See Example 1.]
f has limiting value 7 and passes through (0, 1) and (1, 2).
Solution
general form of logistic equation is f(x) =N/(1+ae-bx), where N is limiting value snd a,b are
constants
f has limiting value 7
f(x) =7/(1+ae-bx)
passes through (0, 1)
1=7/(1+ae0)
1=7/(1+a)
1+a=7
a=6
f(x) =7/(1+6e-bx)
passes through (1, 2).
2 =7/(1+6e-b)
(1+6e-b)=7/2
6e-b=5/2
e-b=5/12
eb=12/5
b=ln(12/5)
f(x) =7/(1+6e-(ln(12/5))x) is the logistic function
![Find the logistic function f with the given properties. HINT [See Example 1.]
f has limiting value 7 and passes through (0, 1) and (1, 2).
Solution
general form of logistic equation is f(x) =N/(1+ae-bx), where N is limiting value snd a,b are
constants
f has limiting value 7
f(x) =7/(1+ae-bx)
passes through (0, 1)
1=7/(1+ae0)
1=7/(1+a)
1+a=7
a=6
f(x) =7/(1+6e-bx)
passes through (1, 2).
2 =7/(1+6e-b)
(1+6e-b)=7/2
6e-b=5/2
e-b=5/12
eb=12/5
b=ln(12/5)
f(x) =7/(1+6e-(ln(12/5))x) is the logistic function](https://image.slidesharecdn.com/findthelogisticfunctionfwiththegivenproperties-230703180822-f31b26c9/85/Find-the-logistic-function-f-with-the-given-properties-HINT-See-Ex-pdf-1-320.jpg)
