Answer: Yes, the given table represents an exponential function [tex]y=e^x.[/tex]
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
[tex]3=3^1,~~~9=3^2,~~~27=3^3,~~~81=3^4,~~~~~etc.[/tex]
Since the values of y are all powers of 3, so let us consider that the exponential function is written as :
[tex]y=3^k.[/tex]
We have
If x = 1, then [tex]y=3^1=3,[/tex]
If x = 2, then [tex]y=3^2=9,[/tex]
If x = 3, then [tex]y=3^3=27,[/tex]
IIf x = 4, then [tex]y=3^4=81,[/tex]
. . .
. . .
Thus, the table represent an exponential function [tex]y=e^x.[/tex]
Option (B) is CORRECT.
