Maths for Engineers - 3

Fitting An Exponential Curve

Fitting an Exponential Curve:

Consider the equation y = aebx. Taking on both sides, we get

     log y = log a bx log e

so,     Y = A Bx

Where Y = log y, A = log a and B = b log e.

This is equivalent to straight line fitting. Compute A and B from reduced normal equations

Finally compute a = antilog A and b = B/log e

Fitting a Power Function:

Consider the equation y = axb. Taking on both side we get;

     log y = log a b log x

          Y = A bX

Where Y = log y, A = log a and X = log x.

This is equivalent to straight line fitting. Compute A and B from reduced normal equations

Example-1:

Determine the curve of the form y = axb.which is the best fit to the following data according to the least square principle:-

 

On putting these tabulated value in the normal equations we get;

            

On solving we get;