Question

What exponential function is best fit for the data table?

Answer 1

Answer:

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

$f(x)=3\times 2^{x-2}+4$  (Option A)

Step-by-step 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)

$f(x)=3\times 2^{x-2}-4$

when x=3.

$f(3)=3\times 2^{3-2}-4\\\\f(3)=3\times 2-4\\\\f(3)=6-4\\\\f(3)=2\neq 10$

Hence, option B is incorrect.

C)

$f(x)=\dfrac{1}{3}\times 2^{x-2}+4$

when x=3

$f(3)=\dfrac{1}{3}\times 2^{3-2}+4\\\\f(3)=\dfrac{1}{3}\times 2+4\\\\f(3)=\dfrac{14}{3}\neq 10$

Hence, option C is incorrect.

D)

$f(x)=\dfrac{1}{3}\times 2^{x-2}-4$

when x=3

$f(3)=\dfrac{1}{3}\times 2^{3-2}-4\\\\f(3)=\dfrac{1}{3}\times 2-4\\\\f(3)=\dfrac{-10}{3}\neq 10$

Hence, option D is incorrect.

A)

$f(x)=3\times 2^{x-2}+4$

when x=3.

$f(3)=3\times 2^{3-2}+4\\\\f(3)=3\times 2+4\\\\f(3)=6+4\\\\f(3)=10$

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:

$f(x)=3\times 2^{x-2}+4$

Answer 2

F(x) = 3(2)^(x − 2) + 4