Answer:
[tex]y=2^{1-x}[/tex]
Step-by-step explanation:
Exponential Function
When we need to express the exponential relation between two variables, we use the equation
[tex]y=Cr^{x}[/tex]
where C, r are constants to be determined by using the given points from the table
For x=0, y=2, thus
[tex]2=C.r^{0}=C[/tex]
We find that C=2
The equation is now
[tex]y=2r^{x}[/tex]
Now we use the point x=1, y=1
[tex]1=2r[/tex]
We find that
[tex]\displaystyle r=\frac{1}{2}[/tex]
Thus, the equation is
[tex]\displaystyle y=2\left(\frac{1}{2}\right)^{x}[/tex]
Rearranging
[tex]y=2(2)^{-x}=2^{1-x}[/tex]
The required equation is
[tex]y=2^{1-x}[/tex]
We can easily verify the last two points are also obtained by using the equation
