Answer:
Option C. is the answer.
Step-by-step explanation:
For linear function.
There should be a common difference in y values of the table.
In the table given
2nd term - 1st term = 8 - 4 = 4
3rd term - 2nd term = 16 - 8 = 8
4th term - 3rd term = 32 - 16 = 16
5th term - 4th term = 64 - 32 = 32
So, there is not a common difference in successive terms.
Therefore, the given data don't model a linear function.
For quadratic function
Difference of difference in the values of y should be same.
As we have calculated difference in terms above, so difference of difference will be
8 - 4 = 4
16 - 8 = 8
32 - 16 = 16
Now we find that difference of the difference is also not same. Therefore, data don't model a quadratic function.
For exponential function
For exponential function there should be a common ratio in every successive term.
[tex]\frac{\text{2nd term}}{\text{1st term}}=\frac{8}{4}=2[/tex]
[tex]\frac{\text{3rd term}}{\text{2nd term}}=\frac{16}{8}=2[/tex]
[tex]\frac{\text{4th term}}{\text{3rd term}}=\frac{32}{16}=2[/tex]
We find a common ratio of 2 in each successive term so data represent an exponential function in the form of [tex]T_{n}=a(r)^{x}[/tex]
where a = 4 and common ratio r = 2
[tex]T_{n}=4(2)^{x}[/tex]
Option C. is the answer.
