Example: Brazilian Capybaras | Click here to open an associated Mathcad worksheet: |
Problem. See previous example.
Solution (revisited). Notice that the algebraic problem of solving
2 + (0.002) t 3 = (1.1) t
(abandoned previously) is the same as solving
2 + (0.002) t 3 (1.1) t = 0 .
That is, it is the same as finding a root of the function
Using our graphical observation that the populations appear to be equal somewhere between
Since the value of the function changes sign between
Now we see that the value of f changes sign between
We now see that the root is in the interval between
The method is clear enough: Keep subdividing the one interval on which f changes sign and compute a new value for the table at the midpoint. Eventually, after many iterations of this simple step, we will be able to compute the root to any degree of accuracy. This may seem tedious, but its algorithmic nature makes it an ideal method for use on calculators or computers, which can perform tedious calculations very quickly.
After five more iterations, the root is bracketed between
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