Question

What exponential function is the best fit for the data in the table?

Answer 1

Answer: The correct answer is choice D.

There are multiple ways to get to the right answer. You could plot the points on a graphing calculator. Then, graph each function to determine which equation matches the points.

You could also input the x values and see which equation produces the y values in the chart. 

On thing to notice is the we have negative output values, there we need to pick either B or D, so the values go beneath the x-axis.

Answer 2

Answer:

option D.

Step-by-step explanation:

Data given in the table is

x           2         3          4

f(x)       -3        0          12

Now we will plug in the values of x in the given functions to find the correct exponential function.

For x =2

A). f(x) = 4(4)$^{(x-1)}$ + 4

     f(2) = 4(4)$^{2-1}$ + 4 = 4 × 4 + 4 = 20

B). f(x) = 4(4)$^{(2-1)}$ - 4

    f(2) = 4(4)$^{2-1}$ - 4 = (4)(4) - 4 = 16 - 4 = 12

C).  f(x) = 1/4(4)$^{x-1}$ +4

      1/4(4)$^{2-1}$ + 4 = $\frac{1}{4}$ × 4 + 4

     = 1 + 4 = 5

D). f(x) = $\frac{1}{4}(4)^{x-1}-4$

     f(2) = $\frac{1}{4} (4)^{2-1}-4=\frac{1}{4}(4)-4$

      = 1 - 4 = -3

We find option D in which f(2) = (-3). so the answer would be option D.