Modelling an Exponential Curve

[ProPM]

Hi guys,

I need to model a curve and I am trying to come up with an exponential equation. I have several points I can work with and this is what I tried so far. (I want to know if this is the correct method or if there is a more precise way to go about this)

I am working on something of the format: a*b^t

My first point in the graph will be when t = 0, hence, I presume the best pick for my value of a would be my first y coordinate point in the graph: 554.8

My doubt arises from this point on:

When I have 554.8*b^t should I set up a pair or simultaneous equations or can I say that b is equal to the "rate of growth of my graph"? That is, if my y coordinate points are 609, 657.5 my rate of growth would be (657.5/609)

Since my graph is not a perfect exponential fit I was thinking of adding a constant:

a*b^ct

But that's something different.

Thanks,
ProPM

 

[hotvette]

I'd probably use y = ae^bt and use two points to determine a and b. A trick is to take the natural log of both sides so you end up with a linear equation. A more elaborate method (if the points have noise and don't fit a curve perfectly) would be a least squares approach, but that's much more involved (especially in the category of precalculus).