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Guessing the Graph

Age 14 to 16 Challenge Level:

 

When analysing scientific data, we often need to suggest a curve to fit a set of points, and deduce the equation of the curve.

In the interactivity below, you can access the results of a scientific experiment, but you can only access one measurement at a time, chosen at random by the computer.

By plotting the points you are given, can you sketch a curve representing the relationship between the two variables?

The data were recorded in three sets, A, B and C, beginning at three interesting points in the experiment, so you may wish to investigate each set separately. Alternatively, you can choose to investigate the combined datasets.
Click on "Go" to see a new piece of data.

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Please see http://nrich.maths.org/techhelp/#flash to enable it.


Can you come up with a possible relationship using only a few pieces of data?

Use the interactivity to get a few data points. Plot them on a set of axes and try to fit a curve to the data.

Generate some more values - do they fit your curve? Draw a new curve in a different colour if you want to change your original "best fit".

Once you are satisfied that your curve represents the data well, try working out an approximate equation for your curve, perhaps using a spreadsheet.

What sort of experiment do you think generated the data?
What sort of scientific questions might be answered by using the graph?
Based on your idea of what the experiment was, why do you think the maximum points of curves B and C are lower than the maximum point of curve A?