Abiologist took a count of the number of migrating waterfowl at a particular lake and recounted the lake’s population of waterfowl 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 waterfowl at the lake on week 8week0123456population635644 7198601,067 1,3401,679

Answer-

The number of waterfowl at the lake on week 8 is 2555

Solution-

Taking

x = input variable = time in week 

y = output variable = population of waterfowl

The general best fit equation in Quadratic Regression is,

Where,

And

Putting the values in the formula and calculating the values from the table we get,

a = 33, b = -24, c = 635

Therefore, the best fit curve is,

We can calculate the population of waterfowl on 8 week, by putting x = 8

Therefore, the number of waterfowl at the lake on week 8 is 2555.