Equation: Exponential growth

Introduction

This equation describes the growth with a constant doubling time.

Entering data

Create an XY data table. Enter time into X, and response (cell number ..) into Y. If you have several experimental conditions, place the first into column A, the second into column B, etc.

After entering data, click Analyze, choose nonlinear regression, choose the panel of exponential equations, and choose Exponential growth.

Consider constraining Y0 to a constant value

The parameter Y0 is the Y value at time zero. In many cases, you will know this value precisely. If so, you should constrain that parameter to be a constant value. To do this, go to the Constrain tab of the nonlinear regression dialog, set the drop down next to Y0 to "Constant equal to" and enter its value.

Model

Y=Y0*exp(k*X)

Y0 is the Y value when X (time) is zero. It is expressed in the same units as Y,

K is the rate constant, expressed in reciprocal of the X axis time units. If X is in minutes, then K is expressed in inverse minutes.

Tau is the time constant, expressed in the same units as the X axis. It is computed as the reciprocal of K.

Doubling-time is in the time units of the X axis. It is computed as ln(2)/K.