Question

Graph the data in the table below which kind of function best models the data write and equation to model the data

Answer 1

The answer is C

all of them plugged in as x work

Answer 2

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.

$\frac{\text{2nd term}}{\text{1st term}}=\frac{8}{4}=2$

$\frac{\text{3rd term}}{\text{2nd term}}=\frac{16}{8}=2$

$\frac{\text{4th term}}{\text{3rd term}}=\frac{32}{16}=2$

We find a common ratio of 2 in each successive term so data represent an exponential function in the form of $T_{n}=a(r)^{x}$

where a = 4 and common ratio r = 2

$T_{n}=4(2)^{x}$

Option C. is the answer.