Wed, 01 May 2024 15:24:40 +0000

For exponential growth/decay, my textbook likes to use \[A(t)=A_0e^{kt}\] as an all-purpose model. They refer to \(k\) as the "growth rate," without talking about units.

This is so confusing. If a quantity increases by, say, 80% every day, that makes it sound like \(k\) should be 0.80. But no, in order to represent an 80% increase per [time unit] in this model, \(k\) would have to be about 0.5878. How is that the "growth rate"?

I prefer to use \[A(t)=A_0(1+k)^{t/T}.\] The \(T\) is the time span in which there is growth of \(100k\%\). (Most of the time, \(T=1\).) But of course, many of my students rely on the textbook for support, so my approach and theirs just confuse them further. 🤦‍♂️