SOLUTION: Find the logistic function that satisfies the given conditions. 15) Initial value = 35, limit to growth = 140, passing through (1, 56)

Algebra ->  Rational-functions -> SOLUTION: Find the logistic function that satisfies the given conditions. 15) Initial value = 35, limit to growth = 140, passing through (1, 56)      Log On


   

Question 1131999: Find the logistic function that satisfies the given conditions.
15) Initial value = 35, limit to growth = 140, passing through (1, 56)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find the logistic function that satisfies the given conditions.

given:
Initial value = 35
limit to growth = 140,
passing through (1, 56)

Use the logistic model:

f%28x%29=c%2F%281%2Ba%2Ab%5Ex%29
f%280%29=35=> at (0,12)
limit to growth => c=140
35=140%2F%281%2Ba%2Ab%5E0%29
35=140%2F%281%2Ba%2A1%29
35=140%2F%281%2Ba%29
35%281%2Ba%29=140
35%2B35a=140
35a=140-35
35a=105
a=105%2F35
a=3

so far:
f%28x%29=140%2F%281%2B3%2Ab%5Ex%29

if passing through (1, 56) , we have
56=140%2F%281%2B3%2Ab%5E1%29
56=140%2F%281%2B3%2Ab%29
56%281%2B3%2Ab%29=140
56%2B168b=140
168b=140-56
168b=84
b=84%2F168
b=1%2F2

=> f%28x%29=140%2F%281%2B3%2A%281%2F2%29%5Ex%29