Find the Exponential Equation y=ab^x Using 2 Points | Easy Method!

Added: 2026-05-16

[00:00:00]so we're given these two points -2 comma 2 9 and 1 comma 6 and we want to write an exponential equation in this form y = a * B to the X power well when you have two variables or two unknowns Like A and B you're going to need two equations to solve for those two unknowns so let's go ahead and write our two equations so I'm going to say this is our X and Y X and Y so we can see that uh when Y is 2 9 x X is -2 that's one equation and we can see here when Y is 6 uh X is 1 so we have two equations this is our system that we want to solve what I would do is I would solve for one of these variables like for example if I solve for a uh we could divide both sides by B so you can see that a is equal to 6 / B and since we know what a is let's put that in terms of a in this other equation so we have 2 9ths is equal to 6 / B * B the -2 right so now when we simplify here what do we do well we've got 2 9th equal 6 * B to the -3rd remember when you divide you subtract the exponents -2 - 1 is -3 and let's go ahead and uh divide both sides by six or we can multiply both sides by 1 16 so that comes out to 254s is equal to B the -3rd which you could reduce this to 1 over 27 is equal to uh 1 over B 3r remember the negative exponent you can take the reciprocal so that means that if we take the reciprocal of both sides of this equation B Cubed is equal to 27 and if we take the cube root we're getting B is equal to 3 now if we take three put it back in for B here that's 6 / 3 which means that a is equal to 2 okay so now we have our A and B so let's go ahead and write our equation we've got y = a which is 2 * B which is 3 to the X power now if you want to check your work you can plug in -2 and see that you get back 29 so if you put in one you can see that you get back six and you got it so if you want to see another example I did talking about how to write these uh exponential equations follow me over to that video I did right there and we'll get some more practice I'll see you there