Linearization of Inverse Proportionality

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SUMMARY

The discussion focuses on the challenge of linearizing data that exhibits inverse proportionality to estimate the half-life of foam. The user attempted to transform y-values into their corresponding 1/y values but did not achieve a linear relationship. Suggestions include exploring logarithmic transformations of the data. The conversation highlights the importance of accurate measurements, particularly when foam height is less than 0.5 cm, as these points introduce significant uncertainty in the analysis.

PREREQUISITES
  • Understanding of inverse proportionality in data analysis
  • Familiarity with scatter plot interpretation
  • Knowledge of logarithmic transformations in data linearization
  • Basic skills in measurement accuracy and uncertainty analysis
NEXT STEPS
  • Research methods for linearizing inverse proportional relationships
  • Learn about logarithmic transformations and their applications in data analysis
  • Explore techniques for improving measurement accuracy in experimental data
  • Investigate statistical methods for assessing uncertainty in data points
USEFUL FOR

Students and researchers in the fields of physics, chemistry, and materials science who are working with experimental data and need to analyze relationships between variables, particularly those involving inverse proportionality.

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Homework Statement



Dear All,

I currently have a set of data which, when plotted on a scatter diagram, proves an inverse proportionality between two sets of data. (Please see attachment.)

I now need to linearize the graph as to estimate the half-life of the foam.


Homework Equations




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The Attempt at a Solution



I tried to transform all y-values (y) into their corresponding 1/y values, thinking that inverting an inverse proportionality should have yielded a linear one, but it didn't help... Suggestions?
 

Attachments

  • foam.jpg
    foam.jpg
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Have you tried the log of the function yet?
 
I get this..
 

Attachments

  • foam.jpg
    foam.jpg
    15.1 KB · Views: 453
Hmm... May I see the data sets?
 
It is only the last few points, beyond 20s, that deviate from a fairly good straight line and these points are probably the ones with greatest uncertainty...when the height of the foam is less than 0.5cm (5mm)...could you actually make these measurements to better than 1mm?
 

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