Graphing Log-Linear Analysis of 2 Exponential Functions

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SUMMARY

The discussion focuses on graphing the relationship defined by the equation V = Cexp(-t/B) + Aexp(-t/S) on log-linear graph paper. The user seeks to determine the parameters B and S from the graph, which complicates the process compared to a single exponential function. The key insight is to plot V against s, leveraging the transformation t = ln(s) to achieve a linear representation. This approach allows for the extraction of both parameters from the combined exponential functions.

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  • Understanding of exponential functions and their properties
  • Familiarity with log-linear graphing techniques
  • Basic knowledge of parameter estimation in mathematical modeling
  • Ability to manipulate logarithmic equations
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Mathematicians, data analysts, and researchers involved in modeling exponential relationships and those interested in advanced graphing techniques for parameter estimation.

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I need to graph a relationship that is the combination of 2 exponential functions on log-linear graph paper.

I have: V = Cexp(-t/B) + Aexp(-t/S)

If it were simply V = Cexp(-t/B) then this wouldn't be a problem (by graphing log(V) = (-1/B)log(e)t + log(C) ) but I need to determine both the B and S parameters (possibly from the same graph). How can i do this?
 
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If t=ln(s), then V is linear in s...

Plot V vs. s.
 

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