00:01
So in this problem, we're asked to find the exponential equation, a relationship.
00:11
It goes through the points minus 1, 32, and 2 .12.
00:20
So let's graph these for just a second, so we can think about what's happening here.
00:24
Here's x and y.
00:25
Remember an exponential is y equals br to the x is the general form.
00:32
So at minus 1 for x, we're way up here at 32 at this point.
00:39
And then when we get over here to 2, we're down here at 12.
00:46
Down here.
00:48
And so this thing graphs like this, doesn't it? as an exponential.
00:57
It keeps going.
00:59
Okay.
01:01
So, first of all, we know that the ratio r.
01:09
We can set up with these two outputs, can't we? because we can set this up as y1 is equal to br to the x1 divided by y2 is br to the x2.
01:35
Just take the ratio of the two functions here.
01:42
Okay? and we know this is going to equal one, right? so, when we do this, the b canceled, so i don't have to worry about it.
01:56
And so what do i end up with? i end up with, this gives me that y1 over y2 is equal to r to the x1 minus x2.
02:09
Okay.
02:11
Well, let's set this up as x1, y1, and x2, y2, just for simplicity.
02:21
So then that means that i have 12 over 32 is equal to r to the 2 minus a negative 1.
02:38
Okay.
02:39
Well, 12 over 32, i can divide both of those by 4.
02:43
So this is 3 over 8 is r to the 2 minus minus that's plus cubed.
02:51
Which means that r is the cubic root of 3, because i'm going to take the cubic root of both sides, 2 of the 8, or 8 is 2 cubed.
03:04
So this is over 2.
03:07
So there's my r...