Question

=

Write an exponential function y = abx whose
graph passes through the points (1,6), (2, 18)

Answer 1

`2(3) {}^(x)`

Explanation:

`y = ab {}^(x)`

We know that when x=1, y=6

`6 = a {b}^(1)`

x=2, y=18

`18 = a {b}^(2)`

Notice that if we divide

`\frac{ {ab}^(2) }{ab} = b`

So if we divide 18 and 6, that will give us our common ratio.

`(18)/(6) = 3`

So our common ratio is 3.

So know we have

`a(3) {}^(x)`

Plug in one of the points to find a.

`6 = a(3)`

`a = 2`

So the equation. we have

`2 * ({3}^(x) )`