Question

A biologist took a count of the number of fish in a particular lake and recounted the lake’s population of fish each of the next six weeks.
Week 0 1 2 3 4 5 6
Population 350 353 382 437 518 625 758

Find a quadratic function that models the data as a function of x, the number of weeks. Use the model to estimate the number of fish at the lake on week 8.

(1 point)


•P(x) = 13x2 – 10x + 350; 917 fish
•P(x) = 13x2 – 10x + 350; 1,102 fish
•P(x) = 18x2 + 10x + 300; 1,252 fish
•P(x) = 18x2 + 10x + 300; 1,532 fish

Answer 1

The correct answer is:

P(x) = 13x² – 10x + 350; 1,102 fish

Explanation:

I plotted this data in a graphing calculator. The screenshot is attached. You can see the curve of the parabola in the graph. I then ran the quadratic regression; again, the screenshot is attached. It lists the values of a, b and c for the equation y = ax²+bx+c.

Answer 2

The correct answer to this question is "P(x) = 13x2 – 10x + 350; 1,102 fish."

Start by plugging 0 into the equation and see which ones give you 350 back. Those equations are the right ones.

Once you find the right equation(s) plug 8 in for x and that will give you the second answer.