# Fitting An Exponential Curve

**Fitting an Exponential Curve:**

Consider the equation y = ae^{bx.} 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 = ax^{b}. 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 = ax^{b}.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;