Question 69063: I have 61 horizontal lines; call them 1 through 61. Line 1 and line 61 are 375mm apart. I need to find the formula so that the distance between the lines increases by an exponential amount over the 375mm, the result being that the distance between 1 and 61 comes out at 375. That is the distances between lines increases, but by the same factor, until 61 is at 375mm.
I hope I have explained this clearly.
Thank you very much.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I have 61 horizontal lines; call them 1 through 61. Line 1 and line 61 are 375mm apart. I need to find the formula so that the distance between the lines increases by an exponential amount over the 375mm, the result being that the distance between 1 and 61 comes out at 375. That is the distances between lines increases, but by the same factor, until 61 is at 375mm.
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You want an exponential function of the form y=ab^x
You have two points of the function: (1,1) and (61,375)
You need to find a and b.
Plug in the point values to get two equations:
1st: 375=ab^(61)
2nd: 1 = ab^1
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Divide the 1st be the 2nd to get rid of the "a's":
375= b^60
Solve for b:
b=375(1/60)=1.10382575...
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Substitute that back into 2nd to solve for "a"
1=a(1.10382575...)
a=0.905940...
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EQUATION:
y=(0.905940)(1.10382575...)^x
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Cheers,
Stan H.
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