I have a question about a Khan Academy problem for determining an exponential function formula based on information from a graph.
The problem: $h(x)= a \times r^x$
We are given two points. (-2, 4.5) and (0,8)
I'm having a problem with one of the steps in the hints section. It's not all clear to me what they did to get the value. I'll explain:
Firstly we know that the 8 in (0,8) is going to be our "a" in the formula.
The problem I'm having is when we plug the next set of points into the equation.
$4.5 = 8 \times r^{-2}$
$\frac{9}{2} = \frac{8}{r^2} $
I understand how the right side gets converted to $8/r^2$ but I don't understand why 4.5 gets multiplied by 2 when all we did on the right side was convert $r^-2$ to $1/r^2$ and multiply by 8. There's no details associated with the any of the 4 steps that they work out and I've been racking my brain trying to figure out a solution with no luck. Any help is greatly appreciated.
As $4.5 = \frac{9}{2}$
So,
$\frac{9}{2} = \frac{8}{r^2}$
Cross multiply terms.
$9 * r^2 = 8 * 2$
$9 * r^2 = 16$
$r^2 = \frac{16}{9}$
$r = \sqrt{\frac{16}{9}}$
$r = \frac{4}{3}$