00:01
In this question, we need to write down exponential equation.
00:05
Y equals a, b, power x.
00:08
This graph passes through 0, 1 over 3, and passes through another point 2 and 3.
00:14
So in order to be able to write down the exponential function like y equals 2 par x or y equals 3 power x minus 1, we need to find the values of a and b first.
00:26
How can we do that? if we have two unknowns, we have to have two equations.
00:29
So we need to substitute with x and y twice, x and y for the first point, and x and y for the second point.
00:37
So let's start by the first point, 0 and third.
00:41
If we substitute x and y in this equation instead of x and y here, we have 1 over 3 equals a, b power 0.
00:55
Having a power 0 makes it easier since b power 0 could be cancelled because any number power 0 is 1.
01:03
So as if you're saying a times 1, which is actually a.
01:07
So now we know the value of a, a equals third.
01:12
Let's use the second point, 2 and 3, and plug x and y.
01:19
Here again, x and y...