Answer :
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].