Question

The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function ​f(x)equalsnegative 3.439 x Superscript 4 Baseline plus 35.952 x cubed minus 99.139 x squared plus 41.541 x plus 178.192 where x is the number of years since 1996. Find the number of bald eagles in the state in the winter of 1999.

Answer 1

The number of bald eagles in the state in the winter of 1999 = 102.709 = 103 to the nearest whole number.

Or 102 if the fractional bird shouldn't be rounded up.

Explanation:

The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function f(x)

N = f(x) = -3.439x⁴ + 35.952x³ - 99.139x² + 41.541x + 178.192

where x = number of years since 1996

The number of bald eagles in the state in the winter of 1999?

1999 is 3 years from 1996, hence, x = 3

N = f(x) = -3.439x⁴ + 35.952x³ - 99.139x² + 41.541x + 178.192

We then put x = 3 into the quartic function that models the number of bald eagles in that state during the winter to get the number of bald eagles in the state in the winter of 1999.

N = f(3) = -3.439(3⁴) + 35.952(3³) - 99.139(3²) + 41.541(3) + 178.192

N = f(3) = (-3.439×81) + (35.952×27) - (99.139×9) + (41.541×3) + 178.192 = 102.709 = 103 to the nearest whole number

Hope this Helps!!!