Question

Find the equation for the exponential function (2,162)(3,486)

Answer 1

Answer:

$y = 2( {3}^{x + 2} ) \: or \: y = 18( {3}^{x} )$

Step-by-step explanation:

The given ordered pair is (2,162)(3,486).

Let the equation be

$y = a {(b}^{x} )$

when x=2, y=162

This gives:

$162 =a {b}^{2}$

Also when x=3, y=486,

$486=a {b}^{3}$

Divide the second equation by the first,

$\frac{a {b}^{3} }{a {b}^{2} } = \frac{486}{162} \\ \implies \: b =3$

When b=3, we have

$162 = a( {3}^{2} ) \\ a = \frac{162}{ {3}^{2} } \\ a = 18$

The exponential equation is:

$y = 18( {3}^{x} )$

$y = 2 \times {3}^{2} ( {3}^{x} ) \\ y = 2( {3}^{x + 2} )$