How do I find the equation of an exponential equation with 2 points? (1,8) and (1,2) Thanks!

Question

tkhunny · Answer

You need an exponential equation with two parameters.  However, as these have the same x-value, this could be a challenge.

How about $x = e^{0\cdot y}$ - I'm going to guess that is not what is wanted, but that makes it no less correct.

anonymous · Answer

I'm not sure what you mean tkhunny? I remember the equation being y = a*B^x I believe

zepdrix · Answer

Tachi, did you write down the coordinate pairs correctly?
Because what you have written can not represent y as a function of x.

anonymous · Answer

Oh, wait sorry. (-1,8) and (1,2) My mistake!

zepdrix · Answer

Ah ok :)

zepdrix · Answer

Ok so the form that you provided looks good.
We'll use the coordinate pairs to figure out our a and b.

zepdrix · Answer

If we plug in the coordinate pairs, we get a system of equations.$$\Large 8=aB^{-1}$$$$\Large 2=aB^1$$

Understand how I set those up?

zepdrix · Answer

Crap I need to leave for class :( Lemme just rush through and give you some notes so you can solve this.

zepdrix · Answer

Divide the first equation by the second.$$\Large \frac{8}{2}=\frac{aB^{-1}}{aB^1}$$The a's will cancel out, allowing you to solve for B.

zepdrix · Answer

After you have found your B, plug it into this form:$$\Large y=aB^x$$Then plug in one of your coordinate pairs in order to solve for a.

anonymous · Answer

ohh, I see. Thanks so much! Those steps are extremely clear and I think I got it!