Continuous exponential growth and misleading rate terminology I'm learning about continuous growth and looking at examples of Continuously Compounded Interest in finance and Uninhibited Growth in biology. While I've gotten a handle on the math, I'm finding some of the terminology counterintuitive. The best way to explain would be through an example. > A culture of cells is grown in a laboratory. The initial population is 12,000 cells. The number of cells, $N$, in thousands, after $t$ days is, $N(t)=12e^{0.86t}$, which we can interpret as an $86\%$ daily growth rate for the cells. I understand the mechanism by which $0.86$ affects the growth rate, but it seems a misnomer to say there's an "$86\%$ daily growth rate" for the cells, as that makes it sound like the population will grow by $86\%$ in a day, when it actually grows by about $136\%$ since the growth is occurring continuously. Is it just that we have to sacrifice accuracy for succinctness?

The instantaneous growth rate is $0.86$ per day in that $N(t)$ is the solution to $\frac {dN}{dt}=0.86N$. You are correct that the compounding makes the increase in one day $1.36$