Question

Which set of ordered pairs could be generated by an exponential function?

(0,0), (1, 1), (2,8), (3, 27)
(0, 1), (1, 2), (2,5), (3, 10)
(0,0), (1,3), (2, 6), (3,9)
(0, 1), (1,3), (2, 9), (3, 27)​

Answer 1

(0, 1), (1,3), (2, 9), (3, 27)

Step-by-step explanation

For an exponential function, there is a common ratio among the terms.

Therefore we need to examine the y-values of the ordered pairs to see which one has a common ratio.

For the first option, the y-values are:

0,1,8,27

`(27)/(8) \\e (8)/(1)`

For the second option, the y-values are:

1,2,5,10

`(10)/(5) \\e (5)/(2)`

For the third option, the y-values are:

0,3,6,9

`(9)/(6) \\e (6)/(3)`

For the last option, the y-values are:

1,3,9,27

`(27)/(9) = (9)/(3) = (3)/(1) = 3`

Since there is a common ratio of 3, the set of ordered pairs (0, 1), (1,3), (2, 9), (3, 27) could generate an exponential sequence.