# Exponential decay/growth

1. Oct 29, 2010

### h00zah

if i have a set of data, where as time increases, so does y, but is bounded by a number say y=c, how do i formulate my equation? how do i find the constants?

i have y=c-a-x*b

this is basically a transformation of y=b*ax+c

2. Oct 29, 2010

### fzero

If you have some reason to believe that

$$y = c - b a^x$$

is the function that fits the (x,y) data, you can compute

$$\ln (c-y) = (\ln a) x + \ln b.$$

If you can find c from the asymptotic form of y, then a plot of $$\ln (c-y)$$ vs x will be linear. You can read $$\ln a$$ from the slope and $$\ln b$$ from the intercept. You can read up on linear regression theory if you want to determine the accuracy of the fit.

3. Oct 29, 2010

### fzero

If you have some reason to believe that

$$y = c - b a^x$$

is the function that fits the (x,y) data, you can compute

$$\ln (c-y) = (\ln a) x + \ln b.$$

If you can find c from the asymptotic form of y, then a plot of $$\ln (c-y)$$ vs x will be linear. You can read $$\ln a$$ from the slope and $$\ln b$$ from the intercept. You can read up on linear regression theory if you want to determine the accuracy of the fit.