Linearization of Inverse Proportionality

AI Thread Summary
The discussion revolves around the challenge of linearizing a dataset that exhibits inverse proportionality to estimate the half-life of foam. The initial attempt involved transforming y-values to their reciprocal, but this did not yield a linear graph. Participants suggest considering logarithmic transformations and request to see the data sets for further analysis. It is noted that the last few data points deviate significantly, raising concerns about measurement accuracy at lower foam heights. Accurate measurements are crucial for improving the reliability of the results.
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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?
 

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

Attachments

  • foam.jpg
    foam.jpg
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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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