The equation that represents this function is:
Option: C ( C) [tex]F(x)=2^x-1[/tex] )
We are given x and corresponding y-values i.e. y=f(x) in a table form as:
x l 3 l 4 l 5 l 7 l 8 l
f(x) l 7 l 15 l 31 l 127 l 255 l
Hence, we check each of the following options which satisfies these values.
A)
[tex]F(x)=3^x[/tex]
when x=3
we have:
[tex]F(3)=3^3\\\\\\F(3)=27\neq 7[/tex]
Hence, option: A is incorrect.
B)
[tex]F(x)=3x[/tex]
when x=3
we have:
[tex]F(3)=3\times 3\\\\\\F(3)=9\neq 7[/tex]
Hence, option: B is incorrect.
C)
[tex]F(x)=2^x-1[/tex]
when x=3
we have:
[tex]F(3)=2^3-1\\\\\\F(3)=7[/tex]
when x=4, we have:
[tex]F(4)=2^4-1\\\\F(4)=15[/tex]
when x=5, we have:
[tex]F(5)=2^5-1\\\\F(5)=31[/tex]
when x=7, we have:
[tex]F(7)=2^7-1\\\\F(7)=127[/tex]
when x=8, we have:
[tex]F(8)=2^8-1\\\\F(8)=255[/tex]
Hence each of the values are satisfied.
Hence, option: C is correct.
D)
[tex]F(x)=2x+1[/tex]
when x=4 we have:
[tex]F(4)=2\times 4+1\\\\F(4)=9\neq 15[/tex]
Hence, option: D is incorrect.
