Can you find an exponential equation if you only know two points?

Question

I just can't find an answer anywhere and I forgot almost every single thing I learned in algebra.

Answer 1

We all forget things, but remember that it's YOUR education; so hang on to what's important. The general form for an exponential equation is:

 

y = a·b^x

 

Let's say you are given two points, (1,15) and (3,375).  Can you find an exponential equation that passes through them?  Step one is to plug the given (x,y) values into the general form of the equation:

 

y = a·b^x

15 = a·b¹

375 = a·b³

 

Now take their ratio:

 

375/15 = (a·b³)/(a·b¹)

25 = b³/b¹

25 = b²

5 = b

 

So our equation so far is y = a·5^x.  To find the value of a, plug in either given point.  I'll use (1,15):

 

y = a·5^x

15 = a·5¹

15 = 5a

3 = a

 

The final equation is y = 3·5^x

Answer 2

f(x) = ab^x

Using the two ordered pairs create two "versions" of the function.

Solve the system.