Find the formula for an exponential function that passes through the two points give. (X,Y) = (-1,3/2) and (X,Y) = (3,24)

Answer:[tex]y=3(2)^{x}[/tex]Step-by-step explanation:Given.Two points are given.[tex](x, y)=(-1,\frac{3}{2})[/tex] and [tex](x, y)=(3,24)[/tex]An exponential function is in the general form.[tex]y=a(b)^{x}[/tex]-------(1)We know the points  [tex](-1,\frac{3}{2})[/tex] and [tex](3,24)[/tex]put the first point value in equation 1[tex]\frac{3}{2}=a(b)^{-1}[/tex][tex]\frac{3}{2}=\frac{a}{b}[/tex][tex]a=\frac{3}{2}\times b[/tex]--------(2)put the second point value in equation 1[tex]24=a(b)^{3}[/tex]----------(3)Put the a value from equation 2 to equation 3[tex]24=\frac{3}{2}\times b(b)^{3}[/tex][tex]b^{3+1}=\frac{24\times 2}{3}[/tex][tex]b^{4} = 16\\b=\sqrt[4]{16} \\b=2[/tex]Put the b value in equation 2[tex]a=\frac{3}{2}\times 2[/tex][tex]a=3[/tex]Put the a and b value in equation 1[tex]y=3(2)^{x}[/tex]So, the exponential function that passes through the points  [tex](-1,\frac{3}{2})[/tex] and [tex](3,24))[/tex] are [tex]y=3(2)^{x}[/tex].