How do you Find the exponential growth rate for a given data set?
1 Answer
The quick answer is: Take logs and find the slope.
Explanation:
If your data is exponential, then the log of the data will be linear.
If the data set is exact, then the log of the data set will exactly fit a line with equation
Slope
where
For example, consider the data:
#f(0) = 3#
#f(2) = 12#
#f(3) = 24#
#f(7) = 384#
Taking natural logs we find:
#ln(f(0)) ~~ 1.0968#
#ln(f(2)) ~~ 2.4849#
#ln(f(3)) ~~ 3.17805#
#ln(f(7)) ~~ 5.95064#
Hence slope
If the data set is inexact (e.g. measurements from an experiment), then take logs before performing a linear regression or similar.