Question

What exponential function is best fit for the data table?

x f(x)
3 10
4 16
5 28

A) f(x) = 3(2)x − 2 + 4

B) f(x) = 3(2)x − 2 − 4

C) f(x) = 1/3(2)x − 2 + 4

D) f(x) = 1/3(2)x − 2 − 4

Answer 1

f(x) = 3(2)^(x − 2) + 4

Answer 2

Hence, the exponential function that best fits the data is:

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

Explanation:

We are given a set of values as:

x f(x)

3 10

4 16

5 28

so we will put the value of x=3 in each of the given options and check which function gives the value 10.

i.e. at x=3 which function f(x)=10.

B)

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

when x=3.

`f(3)=3* 2^(3-2)-4\\\\f(3)=3* 2-4\\\\f(3)=6-4\\\\f(3)=2\\eq 10`

Hence, option B is incorrect.

C)

`f(x)=(1)/(3)* 2^(x-2)+4`

when x=3

`f(3)=(1)/(3)* 2^(3-2)+4\\\\f(3)=(1)/(3)* 2+4\\\\f(3)=(14)/(3)\\eq 10`

Hence, option C is incorrect.

D)

`f(x)=(1)/(3)* 2^(x-2)-4`

when x=3

`f(3)=(1)/(3)* 2^(3-2)-4\\\\f(3)=(1)/(3)* 2-4\\\\f(3)=(-10)/(3)\\eq 10`

Hence, option D is incorrect.

A)

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

when x=3.

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

similarly A option holds for other values of x as well.

Hence, option A is correct.

Hence, the exponential function that best fits the data is:

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