A biologist studied the populations of common guppies and Endler’s guppies over a 6-year period. The biologist modeled the populations, in tens of thousands, with the following polynomials where x is time, in years.%0D%0A%0D%0Acommon guppies: 3.1x2 + 6x + 0.3%0D%0A%0D%0AEndler’s guppies: 4.2x2 – 5.2x + 1%0D%0A%0D%0AWhat polynomial models the total number of common and Endler’s guppies?
To find the polynomial that models the total number of common and Endler's guppies, we need to add the polynomials for each species.
Common guppies: 3.1x^2 + 6x + 0.3
Endler's guppies: 4.2x^2 - 5.2x + 1
Adding the two polynomials together, we get:
(3.1 + 4.2)x^2 + (6 - 5.2)x + (0.3 + 1)
Simplifying, we have:
7.3x^2 + 0.8x + 1.3
Therefore, the polynomial that models the total number of common and Endler's guppies is 7.3x^2 + 0.8x + 1.3.