Question

A biologist took a count of the number of fish in a particular lake, and recounted the lake’s population of fish on each of the next six weeks.

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.


P(x) = 13x^2 – 10x + 350; 917 fish
P(x) = 13x^2 – 10x + 350; 1,102 fish
P(x) = 18x^2 + 10x + 300; 1,252 fish
P(x) = 18x^2 + 10x + 300; 1,532 fish

Answer 1

P(x) = 13x2 – 10x + 350; 1,102 fish

Explanation:

Plug in week 8 for x.

`P(x) = 13 * (8)^(2) - 10(8) - 350 =`

`P(x) = 13 * 64 - 80 + 350 =\\\\ P(x) = 832 - 80 + 350 = 1102`

Answer 2

The two equations for which the given number of fist is satisfied when x = 8 is plugged in are:
P(x) = 13x^2 – 10x + 350
and
P(x) = 18x^2 + 10x + 300

Now, we can only decide which is correct if we have additional information, specifically if we know the number of fish initially. If it is 350, option B is correct and if it is 300 then option D is correct.