An exponential function passing through the given points is required.
The equation is [tex]y=3(2)^x[/tex]
The points are [tex](-3,3/8)[/tex] and [tex](2,12)[/tex]
The exponential equation is of the form
[tex]y=ab^x[/tex]
The equations will be
[tex]\dfrac{3}{8}=ab^{-3}[/tex]
[tex]12=ab^{2}[/tex]
Dividing the equations
[tex]\dfrac{\dfrac{3}{8}}{12}=\dfrac{b^{-3}}{b^2}\\\Rightarrow \dfrac{1}{32}=b^{-5}\\\Rightarrow b^5=32\\\Rightarrow b=32^{\dfrac{1}{5}}\\\Rightarrow b=2[/tex]
Finding [tex]a[/tex]
[tex]a=\dfrac{12}{b^2}\\\Rightarrow a=\dfrac{12}{2^2}\\\Rightarrow a=3[/tex]
The equation is [tex]y=3(2)^x[/tex]
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