exponential growth function in R - fitting data

Question

I have the following data:

> x = 1:40
> y =
 5    6   28   30   31   34   39   48   63   70   82   91  107  112  127  146  171  198  258  334  403  497  571  657  730  883 1024 1139
1329 1635 2059 2545 3105 3684 4289 4778 5351 5916 6729 7600

How can I figure out the exponential function (including the coefficients and constants) of this graph in R?

Answer 1

In your post you have only 38 values for y, so i basically assume x to be 1:38. If y = exp(ax+b), you can change it to log(y) = ax + b and fit a linear model. The below will work with the correct values:

x = 1:38
y = c(5, 6, 28, 30, 31, 34, 39, 48, 63, 70, 82, 91, 107, 112, 127, 
146, 171, 198, 258, 334, 403, 497, 571, 657, 730, 883, 1024, 
1635, 2059, 2545, 3105, 3684, 4289, 4778, 5351, 5916, 6729, 7600
)

fit = lm(log(y) ~ x)
plot(x,y)
lines(x,exp(fitted(fit)),col="blue")