Completing the table of Values. Complete the tables of value.

Answer:Part 1) [tex]a=1[/tex]Part 2) [tex]b=1/16[/tex]Part 3) [tex]c=1/256[/tex] Part 4) [tex]d=1[/tex] Part 5) [tex]e=\frac{4}{9}[/tex]Part 6) [tex]f=\frac{16}{81}[/tex]Step-by-step explanation:we know thatThe function in the orange table is equal to[tex]f(x)=4^{-x}=1/(4^{x})[/tex]sostep 1Find the value of aThe value of a is the value of the function f(x) for [tex]x=0[/tex]Substitute the value of [tex]x=0[/tex] in the function[tex]f(0)=1/(4^{0})=1[/tex]therefore[tex]a=1[/tex]step 2Find the value of bThe value of b is the value of the function f(x) for [tex]x=2[/tex]Substitute the value of [tex]x=2[/tex] in the function[tex]f(2)=1/(4^{2})=1/16[/tex]therefore[tex]b=1/16[/tex]step 3Find the value of cThe value of a is the value of the function f(x) for [tex]x=4[/tex]Substitute the value of [tex]x=4[/tex] in the function[tex]f(4)=1/(4^{4})=1/256[/tex]therefore[tex]c=1/256[/tex]The function in the blue table is equal to[tex]g(x)=(\frac{2}{3})^{x}[/tex]sostep 4Find the value of dThe value of d is the value of the function g(x) for [tex]x=0[/tex]Substitute the value of [tex]x=0[/tex] in the function[tex]g(0)=(\frac{2}{3})^{0}=1[/tex]therefore[tex]d=1[/tex]step 5Find the value of eThe value of e is the value of the function g(x) for [tex]x=2[/tex]Substitute the value of [tex]x=2[/tex] in the function[tex]g(2)=(\frac{2}{3})^{2}=\frac{4}{9}[/tex]therefore[tex]e=\frac{4}{9}[/tex]step 6Find the value of fThe value of f is the value of the function g(x) for [tex]x=4[/tex]Substitute the value of [tex]x=4[/tex] in the function[tex]g(4)=(\frac{2}{3})^{4}=\frac{16}{81}[/tex]therefore[tex]f=\frac{16}{81}[/tex]