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.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.