Answer:
Hence, the exponential function that best fits the data is:
[tex]f(x)=3\times 2^{x-2}+4[/tex] (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)
[tex]f(x)=3\times 2^{x-2}-4[/tex]
when x=3.
[tex]f(3)=3\times 2^{3-2}-4\\\\f(3)=3\times 2-4\\\\f(3)=6-4\\\\f(3)=2\neq 10[/tex]
Hence, option B is incorrect.
C)
[tex]f(x)=\dfrac{1}{3}\times 2^{x-2}+4[/tex]
when x=3
[tex]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[/tex]
Hence, option C is incorrect.
D)
[tex]f(x)=\dfrac{1}{3}\times 2^{x-2}-4[/tex]
when x=3
[tex]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[/tex]
Hence, option D is incorrect.
A)
[tex]f(x)=3\times 2^{x-2}+4[/tex]
when x=3.
[tex]f(3)=3\times 2^{3-2}+4\\\\f(3)=3\times 2+4\\\\f(3)=6+4\\\\f(3)=10[/tex]
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:
[tex]f(x)=3\times 2^{x-2}+4[/tex]
