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January 6th, 2017, 08:31 AM   #1
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Finding an Accurate Exponential Function Equation Given 4 Points

I know I can employ the Generic Exponential Function Formula:

y = a*bt


given two points (t,y) of an Exponential Graph to find an Equation for said Function...

However, when I use the resulting Function Equation for further calculations, the Margin of Error of my results is too large to be acceptable.

In addition to the two (t,y) points used above, I also know two other (t,y) points of the graph; meaning I have a total of 4 known points for the Exponential Graph.

My Question is:

How can I employ All 4 Points in order to obtain a more Accurate Equation for the Exponential Graph?
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January 6th, 2017, 08:36 AM   #2
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conduct an exponential regression using technology ...

ab-Exponential regression Calculator - High accuracy calculation
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January 6th, 2017, 09:20 AM   #3
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Quote:
Originally Posted by Sam202 View Post
I know I can employ the Generic Exponential Function Formula:

y = a*bt


given two points (t,y) of an Exponential Graph to find an Equation for said Function..


However, when I use the resulting Function Equation for further calculations, the Margin of Error of my results is too large to be acceptable.

In addition to the two (t,y) points used above, I also know two other (t,y) points of the graph; meaning I have a total of 4 known points for the Exponential Graph.

My Question is:

How can I employ All 4 Points in order to obtain a more Accurate Equation for the Exponential Graph?
It's not clear what you are asking. Your given exponential formula, has two parameters, a and b. Solving the two equations, setting x and y to the x and y of the points, gives values of a and b such that the curve goes exactly through those two points. Four equations would "over determine" such system.

But if you are asking for a curve, of the form that goes close to four given points, then you want to minimize the "mean square error": where the "" are the four points and you want to find a and b to minimize that.
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January 6th, 2017, 09:46 AM   #4
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Quote:
Originally Posted by Sam202 View Post
. . . the Margin of Error of my results is too large to be acceptable.
How do you define "Margin of Error" and "too large"?
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