# How do you Find the exponential growth function that models a given data set?

##### 2 Answers

This is only a very simplified version!

#### Explanation:

Ok, you can use a program such as Excel that has a function to evaluate the fitting line to a set of data but you can do it by yourself using a general function like:

Where

To evaluate the constants you use your data.

Say that you have values for

For example:

Consider two pairs of data (I invented them):

And

We use them into our basic function to get:

So we get

And

Rearranging:

Take the natural log of both sides to get rid of the exponential:

So finally, the exponential function modelling our data will be:

Suppose that you have experimental data

# y = Ce^(kt) #

where

(NB Equality any equation of the form

Then by taking Natural logarithms of both sides we get:

# lny = ln{Ce^(kt)} #

# " " = lnC + lne^(kt) #

# " " = lnC + kt #

If we write this as:

# lny = kt + lnC#

And compare with the standard equation of a straight lie@

# Y = mX +c #

Hopefully is clear that if we plot

Obviously if plotting the data, does not produce a clear line of best fit then the original assumption about the data being modelled by an exponential function

On other note of caution, In mathematics we would generally choose base

If you would like a solid example let me know and I will find a physics/maths exam question.