00:01
So f of x equals a times b to the x is the general formula for an exponential function, and we want to find the exponential function that goes through these two points here.
00:11
So we're going to go ahead and plug in our values.
00:14
So for 0, 10, our x is 0 and our y is 10.
00:18
So that tells us that 10 is going to equal a times b to the 0.
00:23
Well, b to the 0 equals 1, so that tells us that 10 equals a.
00:28
So our new function is going to be f of x equals 10 times b to the x.
00:32
Now we can plug in our second x and y to figure out what b is going to equal.
00:39
So 40 equals 10 times b to the negative 2.
00:44
Solving for b, we're going to divide both sides by 10.
00:47
So 40 divided by 10 equals 4...