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 January 6th, 2017, 07:31 AM #1 Newbie   Joined: Jan 2017 From: California Posts: 1 Thanks: 0 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?
 January 6th, 2017, 07:36 AM #2 Math Team     Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600 conduct an exponential regression using technology ... ab-Exponential regression Calculator - High accuracy calculation
January 6th, 2017, 08:20 AM   #3
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 Originally Posted by Sam202 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, $y= ab^t$ 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 $y= ab^x$ that goes close to four given points, then you want to minimize the "mean square error": $\frac{1}{4}\left((y_0- ab^{x_0})^2+ (y_1- ab^{x_1}^2+ (y_2- ab^{x_2})^2+ (y_3- ab^{x_3})^2\right)$ where the "$(x_i, y_i)$" are the four points and you want to find a and b to minimize that.

January 6th, 2017, 08:46 AM   #4
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Quote:
 Originally Posted by Sam202 . . . 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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