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January 6th, 2017, 08:31 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, 08:36 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,579 Thanks: 1276 
conduct an exponential regression using technology ... abExponential regression Calculator  High accuracy calculation 
January 6th, 2017, 09:20 AM  #3  
Math Team Joined: Jan 2015 From: Alabama Posts: 2,524 Thanks: 643  Quote:
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.  
January 6th, 2017, 09:46 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 17,524 Thanks: 1318  

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