The function is y = [tex] \frac{1}{3}^{x} [/tex]
This can be found by using the base equation for exponential y = [tex] ab^{x} [/tex]. Now we can use the second ordered pair (0, 1) to find the value of a.
y = [tex] ab^{x} [/tex]
1 = [tex] ab^{0}[/tex]
1 = a(1)
1 = a
Now that we have a, we can solve for b using any other ordered pair.
y = [tex] ab^{x}[/tex]
[tex] \frac{1}{3} [/tex] = [tex] (1)b^{1}[/tex]
[tex] \frac{1}{3} [/tex] = (1)(b)
[tex] \frac{1}{3} [/tex] = b
Now we can use these in the same equation.
y = [tex] \frac{1}{3}^{x} [/tex]
