Given a logistic function, calculate the constant

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Discussion Overview

The discussion revolves around calculating the constant B in a logistic function given the condition f(0)=5. The context is primarily mathematical reasoning related to the evaluation of a specific function.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant presents the logistic function f(t)= (20)/ 1+Be^-1/2t and requests help in calculating B.
  • Another participant confirms the equation format and provides a mathematical representation.
  • There is a suggestion to substitute t=0 and f(t)=5 into the equation to find B.
  • A later reply indicates that after substitution, B is found to be 3, with an expression of satisfaction regarding this result.
  • Another participant agrees with the calculation of B being 3, affirming the correctness of the result.

Areas of Agreement / Disagreement

Participants appear to agree on the calculation process and the resulting value of B as 3, although the initial steps and assumptions are not fully detailed or universally acknowledged.

Contextual Notes

There may be missing assumptions regarding the interpretation of the function and the conditions under which B is calculated, as well as potential ambiguities in the function's notation.

docbrown1
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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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