A biologist studied the populations of black bears and brown bears over a 10-year period. The biologist modeled the populations, in thousands, with the following polynomials where x is time, in years.
black bears: 2.3x^2 – 5.6x + 2.3
brown bears: 2.4x^2 + 7.2x + 0.97
What polynomial models the total number of brown and black bears?
To find the total number of brown and black bears, we simply add the polynomials for black bears and brown bears together.
(2.3x^2 - 5.6x + 2.3) + (2.4x^2 + 7.2x + 0.97)
= 2.3x^2 - 5.6x + 2.3 + 2.4x^2 + 7.2x + 0.97
= (2.3 + 2.4)x^2 + (-5.6 + 7.2)x + (2.3 + 0.97)
= 4.7x^2 + 1.6x + 3.27
Therefore, the polynomial that models the total number of brown and black bears is:
4.7x^2 + 1.6x + 3.27