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.

definitely a. the others have almost all data points on one side of the line.

step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.