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 that
The function in the orange table is equal to
[tex]f(x)=4^{-x}=1/(4^{x})[/tex]
so
step 1
Find the value of a
The 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 2
Find the value of b
The 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 3
Find the value of c
The 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]
so
step 4
Find the value of d
The 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 5
Find the value of e
The 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 6
Find the value of f
The 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]
