Which type of function best models the data in the table? justify your choice.

Quadratic equation:  

Explanation:

We need to find best model of given data in the table.

1) Linear: For linear slope of the line must be same. Slope is change in y over change x must be same. But if we find change in y over change x for this table. They won't be same. This table value can't be linear.

2) Quadratic: For quadratic equation. we will take standard form of quadratic equation . Using any three value of table we will find a, b and c and then we satisfy other value of of table.

Point 1: (4,118)

Point 2: (6,142)

Point 3: (8,150)

Now we have three equation and to solve for a, b and c. Using elimination method we get the value of a=-2, b=32 and c=22.

So, Quadratic equation

So, we get quadratic model for the given data in the table.

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.