Write an exponential function y = ab^x for a graph that includes (–3, 16) and (–1, 4)

Answer:[tex]y=2(\frac{1}{2} )^x[/tex]Step-by-step explanation:Given the exponential function as [tex]y=ab^x[/tex]substitute both points in the equation abovepoint (-3,16) will be [tex]16=ab^{-3}[/tex]point (-1,4) will be[tex]4=ab^{-1}[/tex]make a the subject of the formula in both equations above[tex]a=\frac{16}{b^{-3} } \\\\\\a=\frac{4}{b^{-1} }[/tex]This means[tex]=\frac{16}{b^{-3} } =\frac{4}{b^{-1} }[/tex]Cross multiply as;[tex]16b^{-1} =4b^{-3}[/tex]Divide by 4 both sides to get[tex]4b^{-1} =b^{-3}[/tex]Divide by b^-1 both sides[tex]\frac{4b^{-1} }{b^{-1} } =\frac{4b^{-3} }{b^{-1} } \\\\\\4=b^{-2} \\\\\\4=\frac{1}{b^2} \\\\\\b^2=\frac{1}{4} \\\\\\b=\sqrt{\frac{1}{4} } =\frac{1}{2}[/tex]Find value of a[tex]4=ab^{-1} \\\\4=a*(\frac{1}{2})^{-1}  \\\\\\4=a*2\\\\2=a[/tex]Hence a=2  and b=1/2 thus write the equation as;[tex]y=ab^x\\\\\\y=2(\frac{1}{2} )^x[/tex]