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: 3.1x2 + 6x + 0.3 Endler’s guppies: 4.2x2 – 5.2x + 1 What polynomial models the total number of common and Endler’s guppies?
To find the total number of common and Endler's guppies, we can simply add the two polynomials together:
Total number of guppies = 3.1x^2 + 6x + 0.3 + 4.2x^2 - 5.2x + 1
= (3.1 + 4.2)x^2 + (6 - 5.2)x + (0.3 + 1)
= 7.3x^2 + 0.8x + 1.3
Therefore, the polynomial model for the total number of common and Endler's guppies is 7.3x^2 + 0.8x + 1.3.