The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function f(x)= -3.319x^4+35.976x^3-99.197x^2+41.78 3x+175.773 i am trying to find how many eagles will be around in the winter of 1999

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.

_____

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

_____

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.