00:01
This problem says the graph of an exponential function passes through the points 2 -12 and 3 -9 -24, and we want to find the exponential function that describes this graph.
00:09
And to start, we're going to look at the exponential function form, y equals a times b to the x.
00:15
And what we want to find is our a and b value so that we can write this function.
00:20
And we have two sample points that we could plug in to get some form of relationship between a and b.
00:25
So first we'll plug in the x value of 2 and the y value of 12.
00:30
Which gives us negative 12 for y equal to a times b raised to the second for x and then we also have 3 negative 24 so negative 24 for y equals a times b raised to the third this time for x so a and b are supposed to equal the same value here in both these equations so what i'm going to do is isolate a for both that way i can set the expressions that a is supposed to be equal to together so we can solve for b so i'm going to divide by b squared to get a equal to negative 12 over b squared.
01:03
I'm going to divide by b to the 3rd on the right to get a equal to negative 24 over b to the 3rd.
01:09
So once again, if a equals negative 12 over b squared and negative 24 over b to the 3rd, we can set those expressions equal, and then do what we have to to solve for b.
01:22
And to start solving for b, i'm going to cross multiply...