Question

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

Answer 1

Answer:

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

Step-by-step 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.

$\frac{18}{6} = 3$

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

$2 \times ({3}^{x} )$