SOLUTION: 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. Where the number of weeks is w and t

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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. Where the number of weeks is w and t      Log On


   

Question 1058487: 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. Where the number of weeks is w and the population is p.
(w,p): (0,350) (1,353) (2,382) (3,437) (4,518) (5,625) (6,758)
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.
- I already know that the answer is P(x)=13x^2-10x+350; 917 fish. I just need to know how to get that answer.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use a general quadratic equation and solve using three of the given points.
y=ax%5E2%2Bbx%2Bc
So using (0,350),
350=a%280%29%5E2%2Bb%280%29%2Bc
c=350
(1,353)
353=a%281%29%5E2%2Bb%281%29%2B350
1.a%2Bb=3
(2,382)
382=a%282%29%5E2%2Bb%282%29%2B350
4a%2B2b=32
2.2a%2Bb=16
Subtracting 1 from 2,
2a%2Bb-a-b=16-3
a=13
Then use either equation,
13%2Bb=3
b=-10
So,
y=13x%5E2-10x%2B350