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]