Question

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.
common guppies: 3.1x^2+6x+0.3

Endler's guppies: 4.2x^2-5.2x+1

what polynomial models the total number of common and Endler's guppies

Answer 1

We can say that total number of guppies would simply be the sum of two polynomials.
To get our answers we need to add those two polynomials. We add polynomials by adding their like terms. Like terms are those that have the same exponent.
$3.1x^2+6x+0.3+4.2x^2-5.2x+1=\\=(3.1x^2+4.2x^2)+(6x-5.2x)+(0.3+1)=\\ =7.3x^2+0.8x+1.3$
So the total amount of guppies would be modeled using this polynomial:
$7.3x^2+0.8x+1.3$