Answer :

Answer:

[tex]y=\frac{1}{6} (6)^{\frac{-1}{4} x}[/tex]

Step-by-step explanation:

(-2,6) and (2,1)

format for an exponential function is

y=a *bˣ

plug in the first point

[tex]6=a*b^{-2}[/tex]

plug in second point

1 = a * b²

divide the 2 equations:

[tex]\frac{6}{1}= \frac{a*b^{-2} }{a*b^{2} }[/tex]                >the a's cancel

[tex]\frac{6}{1}= \frac{b^{-2} }{b^{2} }[/tex]                   >use quotient exponent rule subtract

[tex]6=b^{-4}[/tex]                  >solve for b

[tex]6^{-\frac{1}{4} } =b^{-4}^({-\frac{1}{4} } )[/tex]

[tex]b=6^{-\frac{1}{4} }[/tex]

plug in to solve for a

[tex]1=a* 6^{\frac{-1}{4} ^{2} }[/tex]

[tex]1=a* 6^{\frac{-1}{2} }[/tex]

[tex]1^{-2} =a* 6^{\frac{-1}{2 }^{-2 }[/tex]

1=6a

a=1/6

plug back into equation

[tex]y=\frac{1}{6} (6)^{\frac{-1}{4} x}[/tex]