Determine whether the points represent a linear, quadratic, or exponential relationship between x and y. Besides graphing them, how would I solve this?
(0 , -2)
(3 , 7)
(6 , 34)
(9 , 79)

Question

Determine whether the points represent a linear, quadratic, or exponential relationship between x and y. Besides graphing them, how would I solve this?
(0 , -2)
(3 , 7)
(6 , 34)
(9 , 79)

ranga · Answer

The x values go up by 3.
The corresponding y values g up by: (7-(-2)), (34-7), (79-34) or 9, 27, 45

If the relationship between y and x were linear, the y will go up by the same amount each time.  Here it does not.  Therefore, the relationship between y and x is NOT linear.

Next, is it quadratic?

ranga · Answer

Take the differences of the differences:
(27-9) and (45-27)  or 18 and 18.

The second difference is the same.  Therefore, the relationship between y and x is quadratic.

anonymous · Answer

If it was an exponential, what relationship would there be between the y-values?

ranga · Answer

The y values will increase or decrease much more rapidly.  The first differences will not be a constant ruling out linear relationship.  The second differences will not be a constant ruling out quadratic relationship.  The third difference will not be a constant ruling out cubic relationships.  So you try to see if you can fit an equation of the type:
y = a * (b)^x  with the first two points 
(by substituting the first two points you can find a and b)

And then see if you can compute the 3rd, 4th, etc. points.  If you can, then you have found your exponential relationship.

anonymous · Answer

thank you for your help!

ranga · Answer

You are welcome.

anonymous · Answer

A solution using Mathematica is attached.