determine the formula of a dataset

I have a small dataframe that has a exponentially decreasing trend. I would like to extract a formula ba开发者_JAVA百科sed on the data in my dataframe? Is this possible, and if so, how can I go about extracting the formula?

To get a best fit exponential curve, you'll want to basically convert an the curve to a linear one, and find the "linear fit" and then convert it back. For example, here's data decreasing exponentially.

t <- c(0,2,4,7)
y <- c(25,11,4,3)

Then take the log of y.

y2 <- log10(y)

Then model y2 as a function of time.

lm(y2~t)

You'll get the slope and intercept in usual linear equation form (y = mx + b), but using log(y). To get the exponential equation of the line, put the slope and intercept into the following form:

y = A*r^t

Where A = 10^intercept and r = 10^slope.

For these data, your equation will be:

y = 20.77304*0.7333309^t

If you want to plot them together, define:

expLine <- function(t) 20.77304*0.7333309^t

Then plot(t,y) and curve(expLine,0,7,n=101,add=TRUE).