Find the exponential function f(x) = Cax whose graph is given. f(x) = 1 any help with this?
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Originally Posted by kyleu03 Find the exponential function f(x) = Cax whose graph is given. f(x) = 1 any help with this? An exponential equation of this shape will have an equation $\displaystyle f(x)=a(b^{-x})$. Plugging in the two points gives us: $\displaystyle 2=a(b^{-0})$ $\displaystyle \frac{2}{9}=a(b^{-2})$ Solve this system for $\displaystyle a$ and $\displaystyle b$. Spoiler: Solving the first equation give us $\displaystyle a=2$. Plugging into the second equation gives us $\displaystyle \frac{2}{9}=2(b^{-2})\implies \frac{1}{9}=b^{-2}\implies b=3$. So the equation of the curve is $\displaystyle f(x)=2(3^{-x})$.
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