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# Exponential Curves

## Exponential (or asymptotic regression)

Y = a + brX ( Y = a + b * r**X )

(This is the same as another common form of the equation: Y = a + be-kx, with k= -loger).

## Double exponential (different rates)

Y = a + brX + csX ( Y = a + b * r**X + c * s**X )

## Line plus exponential (addition of linear trend)

Y = a + brX + cX ( Y = a + b * r**X + c * X )

A limiting case of the double exponential – an exponential curve with non-horizontal asymptote.

## Critical exponential

Y = a + (b + cX)rX ( Y = a + (b + c * X) * r**X )

Another limiting case of the double exponential.

## Direction of response

For exponential curves the direction of response can be selected. This determines whether the asymptote is to the left or right. The effect of direction on the parameters of the curves is as follows. Exponential, Line plus exponential and Critical exponential: direction right gives r 1.0. Double exponential: direction right gives r,s 1.0.