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The length of six leaves in cm is 2, 4, 6, 8, 10 and 12, and their areas in square cm are 2.1, 8.5…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The length of six leaves in cm is 2, 4, 6, 8, 10 and 12, and their areas in square cm are 2.1, 8.5, 18.2, 31.8, 50.5 and 71.9. Put them in a table, fit a straight line to the logarithms, and find the power in . Is it what you expect?
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. On a log-log graph, a power law is a straight line, and the slope is the power.
Check. The slope is 1.97, close to 2. This is what we expect for similar shapes: if every length of a leaf is made times larger, the area is made times larger. The constant is about 0.54.
Answer: , which is 2 within the scatter. The area of a leaf is proportional to the square of its length.
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