How table of values can be an exponential function?

Answer 1

With a table of value, you first make sure the change in x is constant. Then you look at the ratio of the y's value. If the ratio of the values is the same, then it is an exponential function:

x y

1 120

2 180

3 270

4 405

5 607.5

6 911.25

e.g. 180/120 = 1.5, 270/180 = 1.5, 405/270 = 1.5

Therefore, this is an exponential function. To take the question even further, we can even identify the equation of the exponential function.

y=Ar^x (*note: ^ is the symbol for "to the power of")

A = the first term when x is 0

r = the constant ratio

To find A, we sub in one of the coordinates in the table of value. I choose the coordinate (1, 120).

120 = A(1.5^1)

120/1.5 = A

80 = A

Therefore the equation is: y = 80(1.5^x)

Hope this helps.