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Modifying an equation to plot a straight line. 
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#1
Feb1013, 11:47 PM

P: 91

1. The problem statement, all variables and given/known data
Show all the steps required to modify the equation so that the plot yields a straight line. N/N_{0}=[itex]e\ [/itex]^{ux} This equation demonstrates the fraction radiation absorbed by a material, where "N_{0}" is the number of incident photons from the radioactive source without any absorbed introduced, "N" is the number of transmitted photons, "u" is the absorption coefficient of the absorber (units m^{1}) and x is the thickness of the absorber. 2. Relevant equations 3. The attempt at a solution Subsequently I am instructed to graph lnN/N_{0} vs "x". Therefore I am assuming N/N_{0} will be my "y" value in the equation of the line, whereas "x" (the thickness) will be my "x" value. I tried something along these lines, but have no idea if I am even in the ballpark. N/N_{0}=e^{ux} lnN/N_{0}=ux That seems to give me lnN/N_{0} as "y", u as "m", x as "x" and 0 as "b". Please give me some thoughts. Thank you. 


#2
Feb1113, 12:38 AM

P: 615

Well, do you get a straight line when you plot it? If you do, you're done.



#3
Feb1113, 12:45 AM

P: 91

The problem is that I have no data to plug into the equation and verify it because this is a question that I need to have answered before we do the experiment.



#4
Feb1113, 12:46 AM

HW Helper
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P: 10,344

Modifying an equation to plot a straight line.
ln(N/N_{0})=ux ehild 


#5
Feb1113, 01:23 AM

P: 615




#6
Feb1113, 03:26 PM

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#7
Feb1113, 03:36 PM

P: 615




#8
Feb1113, 03:44 PM

Sci Advisor
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P: 4,300

Note that you can also use the property ln(a/b) = ln(a)  ln(b) to rewrite the equation to ln(N) =  u x + ln(N_{0}) in which case you will get a loglinear plot for N and your starting value "b" will be the initial value N_{0} (although on your logarithmic yaxis, you will actually plot ln(N_{0}). [edit]Here is another example of a logplot: Note how equal distances on the yaxis correspond to multiplications instead of additions, in other words, they've plotted the log_{10} of the actual quantity. (Googled it from http://www.eyephysics.com/tdf/models.htm) 


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