Question

What exponential function is the best fit for the data in the table? xf(x) 310 4 16 5 28 A. f(x) = 3(2)x − 2 + 4 B. f(x) = 3(2)x − 2 − 4 C. f(x) = one third(2)x − 2 + 4 4. f(x) = one third(2)x − 2 − 4

Answer 1

option: A is correct.

`f(x) = 3* (2)^(x-2)+4`

Explanation:

we are given a table of values as:

x 3 4 5

f(x) 10 16 28

The exponential function which is the best fit for the data in the table is:

`f(x) = 3* (2)^(x-2)+4`

since when we put the value of x in the corresponding function we get the values as in the table.

i.e. when x=3

`f(x) = 3* (2)^(3-2)+4=3* 2+4=6+4=10`

when x=4

`f(x) = 3* (2)^(4-2)+4=3* 2^2+4=12+4=16`

when x=5

`f(x) = 3* (2)^(5-2)+4=3* 2^3+4=24+4=28`

Hence, option A is correct.

`f(x) = 3* (2)^(x-2)+4`

Answer 2

We are given of the data in table composed of three points when graphed. We are asked to determine the function that best fits to the data given. Through substitution, the best fit equation is A. f(x) = [3(2)^(x − 2)] + 4.
f(3) = [3(2)^(3 − 2)] + 4 = 10f(4) = [3(2)^(4 − 2)] + 4 = 16f(5) = [3(2)^(5 − 2)] + 4 = 28