Question

17. Does the table represent an exponential function? (1 point)

x | 1 | 2 | 3 | 4 |
-----------------------
y | 3 | 9 | 27 | 81 |

A. No

B. Yes

Answer 1

B. Yes it's an exponential function because the y is increasing rapidly without a constant rate of change

Answer 2

Answer: Yes, the given table represents an exponential function
`y=e^x.`

The correct option is (B) Yes.

Step-by-step explanation: We are given to check whether the following table represents an exponential function or not :

x | 1 | 2 | 3 | 4 |

-----------------------

----------------------------------

y | 3 | 9 | 27 | 81 |

We see that

`3=3^1,~~~9=3^2,~~~27=3^3,~~~81=3^4,~~~~~etc.`

Since the values of y are all powers of 3, so let us consider that the exponential function is written as :

`y=3^k.`

We have

If x = 1, then
`y=3^1=3,`

If x = 2, then
`y=3^2=9,`

If x = 3, then
`y=3^3=27,`

IIf x = 4, then
`y=3^4=81,`

. . .

. . .

Thus, the table represent an exponential function
`y=e^x.`

Option (B) is CORRECT.