Problem

Use the two polynomials suggested in example 1 to predict the number of acres destroyed after 30, 40, and 50 days. It turns out that after 30 days, the number of acres destroyed was 25100. What was the percentage error in each of your estimates? How does this reflect on your choice of modeling function?

Solution

The two polynomials under consideration are

The estimates for future number of acres destroyed by fire are

If the actual number of acres burned after 30 days is 25100, the error in each of these estimates is

y₁ produces a smaller percentage error in absolute value, reinforcing our earlier conclusion that is was in fact the better choice to model the data.