# Exponential decay/growth

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

Related Precalculus Mathematics Homework Help News on Phys.org
fzero
Homework Helper
Gold Member
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.

fzero
Homework Helper
Gold Member
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.