My original post can be found here – this was a favourite practical test.
Additions for 2013. To paraphrase George Orwell, curves are good, straight lines are better. This means that we can learn more about the data with a good straight line than we can with a curve, simply because curves are notoriously difficult to draw well. In exams, they’ll penalise you a mark if your curve is too thick, has a feathery look to the line or it doesn’t go through all the error bars.
How can we determine if a decay is exponential or not? The right way to do this is to plot the ln of the y value against the x value and if the points fall on a straight line within the error bars, the function is an exponential. The other way is less elegant but you’re also expected to know that if a curve is exponential the slope of the y value is proportional to y.
Here’s the trick. Draw tangents to the curve at 3 separate y values. Make the triangles as big as you can. If it’s exponential, the slope divided by the y value will give the same answer, k