MHB Given a logistic function, calculate the constant

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To calculate the constant B in the logistic function f(t) = 20 / (1 + Be^(-1/2t)) given that f(0) = 5, the equation is simplified by substituting t = 0. This results in the equation 5 = 20 / (1 + B), leading to the conclusion that B = 3 after rearranging and solving. The discussion confirms the correctness of the calculation and expresses appreciation for the assistance. The final result shows how to derive B from the logistic function effectively.
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Please help!

f(t)= (20)/ 1+Be^-1/2t

calculate the constant B if f(0)=5
 
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docbrown said:
Please help!

f(t)= (20)/ 1+Be^-1/2t

calculate the constant B if f(0)=5

Hi docbrown, (Wave)

Welcome to MHB!

Is this the equation you wrote? $$f(t)=\frac{20}{1+Be^{-.5t}}$$
 
Jameson said:
Hi docbrown, (Wave)

Welcome to MHB!

Is this the equation you wrote? $$f(t)=\frac{20}{1+Be^{-.5t}}$$

Yes!
 
Is this your function?

$\displaystyle f(t)= \frac{20}{ 1+Be^\frac{-1}{2t}}$
 
Ok, then what we need to do is plug in $t=0$ and $f(t)=5$. What does our equation become when we plug in those two values?

From there we need to simplify but that will come after the above part. :)
 
I was that easy! Thank you very much! B=3 ! :)
 
docbrown said:
I was that easy! Thank you very much! B=3 ! :)

Yep that looks correct. Well done. :)
 

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