Question

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

x f(x)
2 -3
3 0
4 12




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

B. f(x) =4(4)^ x - 1 - 4

C. f(x) = 1/4(4)^x -1 + 4

D. f(x) = 1/4(4)^ x - 1 - 4

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

option D.

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 =
`(1)/(4)` × 4 + 4

= 1 + 4 = 5

D). f(x) =
`(1)/(4)(4)^(x-1)-4`

f(2) =
`(1)/(4) (4)^(2-1)-4=(1)/(4)(4)-4`

= 1 - 4 = -3

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