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.
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)
Responses
P(x) = 13x2 – 10x + 350; 917 fish
P ( x ) = 13 x 2 – 10 x + 350; 917 fish
P(x) = 13x2 – 10x + 350; 1,102 fish
P ( x ) = 13 x 2 – 10 x + 350; 1,102 fish
P(x) = 18x2 + 10x + 300; 1,252 fish
P ( x ) = 18 x 2 + 10 x + 300; 1,252 fish
P(x) = 18x2 + 10x + 300; 1,532 fish
The correct quadratic function that models the data is P(x) = 13x^2 - 10x + 350.
To estimate the number of fish in the lake on week 8, we substitute x = 8 into the function:
P(8) = 13(8)^2 - 10(8) + 350 = 832 - 80 + 350 = 1102 fish.
Therefore, the estimate for the number of fish in the lake on week 8 is 1,102 fish.
Therefore, the correct answer is P(x) = 13x^2 - 10x + 350; 1,102 fish.