Answer:
[tex]2(3) {}^{x} [/tex]
Step-by-step explanation:
[tex]y = ab {}^{x} [/tex]
We know that when x=1, y=6
[tex]6 = a {b}^{1} [/tex]
x=2, y=18
[tex]18 = a {b}^{2} [/tex]
Notice that if we divide
[tex] \frac{ {ab}^{2} }{ab} = b[/tex]
So if we divide 18 and 6, that will give us our common ratio.
[tex] \frac{18}{6} = 3[/tex]
So our common ratio is 3.
So know we have
[tex]a(3) {}^{x} [/tex]
Plug in one of the points to find a.
[tex]6 = a(3)[/tex]
[tex]a = 2[/tex]
So the equation. we have
[tex]2 \times ({3}^{x} )[/tex]
