Question

20. A biologist studied the populations of geckos and salamanders at Huntington Beach State Park overa five year period. The biologist modeled the populations, in thousands, with the following polynomialswhere x is time, in years.

Answer 1

We will be using the summation of polynomials to solve this problem.

We are given two polynomials:

`\begin{gathered} 9.7x^2-0.8x+2.3 \\ -1.1x^2+7.7x+5.4_{} \end{gathered}`

We want to find the total population of both the geckos and the salamanders. Each polynomial represents their population, so we want to add these two polynomials together.

We can do this easily by adding the coefficients of our variables.

For the x² term:

`9.7x^2+(-1.1x^2)=9.7-1.1=8.6x^2`

For the x term:

`-0.8x+7.7x=-0.8+7.7=6.9x`

Finally, for the constants:

`2.3+5.4=7.7`

After we do the addition, we need to combine the terms into one polynomial:

`8.6x^2+6.9x+7.7`

This means that Choice C is our answer.