Why do we include the $e^{k}$?
Wouldn't it be easier to simply use $f(t)=ap^{t}$ where $p$ is the percentage increase per time.
Is there a reason why the convention is to use $f(t)=ae^{kt}$?
2026-04-24 22:28:51.1777069731
Why do we use the form $f(t)=ae^{kt}$ for exponential growth and decay?
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See also: What's so "natural" about the base of natural logarithms?
The choice of base is arbitrary, but the primary reason is likely that the defining equation for the system looks like $$\frac{df}{dt}=kf.$$ This means that the rate of growth of the population is proportional (proportionality $k$) to the population at a given time. The solution is $f(t)=ae^{kt}$. It can be re-expressed as you said, but there is no benefit.