Answer:
[tex] y = 2( {3}^{x + 2} ) \: or \: y = 18( {3}^{x} )[/tex]
Step-by-step explanation:
The given ordered pair is (2,162)(3,486).
Let the equation be
[tex]y = a {(b}^{x} )[/tex]
when x=2, y=162
This gives:
[tex]162 =a {b}^{2} [/tex]
Also when x=3, y=486,
[tex]486=a {b}^{3} [/tex]
Divide the second equation by the first,
[tex] \frac{a {b}^{3} }{a {b}^{2} } = \frac{486}{162} \\ \implies \: b =3 [/tex]
When b=3, we have
[tex]162 = a( {3}^{2} ) \\ a = \frac{162}{ {3}^{2} } \\ a = 18[/tex]
The exponential equation is:
[tex]y = 18( {3}^{x} )[/tex]
[tex]y = 2 \times {3}^{2} ( {3}^{x} ) \\ y = 2( {3}^{x + 2} )[/tex]
