Answer:
about 111
Step-by-step explanation:
We presume the function uses x = years after 1996, so 1999 corresponds to x=3. Put 3 where x is in the function and evaluate. The result of 110.9 can be rounded to the nearest integer, since we're talking about a count of eagles.
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Methods
When doing this by hand, I find it convenient to rewrite the function so it is in Horner Form:
... f(x) = (((-3.319x +35.976)x -99.197)x +41.783)x +175.773
Then, you're not evaluating high powers of anything, and you're generally multiplying reasonable-size numbers. This evaluates as ...
... f(3) = ((26.019·3 -99.197)3 +41.783)3 +175.773
... = (-21.140·3 +41.783)3 +175.773
... = -21.637x +175.773
... = 110.862
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This same form can be used to write a function that a graphing calculator or spreadsheet can evaluate. I find it convenient to do that, as it makes it easier to correct any mistakes in entering 5 multi-digit numbers.
