Answer:
The correct option is C). f(x)=[tex]4\times (\frac{1}{2})^{x}[/tex]
Step-by-step explanation:
Given table show value of y=f(x) with respect to value x.
Table:
X Y
0 4
1 2
2 1
By looking at given options,
Let f(x)=[tex]a\times b^{x}[/tex]
Now, Using a given table values.
When x=0, f(x)=4
f(x)=[tex]a\times b^{x}[/tex]
f(0)=[tex]a\times b^{0}[/tex]
4=[tex]a\times1[/tex]
a=4
When x=1, f(x)=2
f(x)=[tex]a\times b^{x}[/tex]
f(1)=[tex]a\times b^{1}[/tex]
also, a=4
2=[tex]4\times b^{1}[/tex]
2=4xb
b=[tex]\frac{1}{2}[/tex]
Replacing value of a and b in f(x)
we get,
f(x)=[tex]4\times (\frac{1}{2})^{x}[/tex]
The correct option is C). f(x)=[tex]4\times (\frac{1}{2})^{x}[/tex]
