Linearization of Inverse Proportionality

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Homework Help Overview

The original poster discusses a set of data that demonstrates an inverse proportionality between two variables, seeking to linearize the graph to estimate the half-life of a foam. The context involves data analysis and transformation techniques.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to transform y-values into their corresponding 1/y values to achieve linearization but finds this approach ineffective. Some participants suggest considering the logarithm of the function as an alternative method. Others inquire about the data sets and the precision of measurements at lower values.

Discussion Status

The discussion includes various approaches to linearization, with participants exploring different methods and questioning the reliability of certain data points. There is no explicit consensus, but suggestions for further exploration have been made.

Contextual Notes

The original poster notes that the last few data points, which deviate from a linear trend, may have significant uncertainty, particularly when the height of the foam is below a certain threshold. This raises questions about measurement accuracy and the implications for the analysis.

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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: 464
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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