what is the purpose of the value e?
In: Mathematics
It’s the value of C where the gradient of the curve C^x is equal to C^x .
In other words at e^x the rate of growth/decay is equal to the size of the population/sample.
For other values of C^x there are modifiers you have to do to calculate the gradient.
In practical terms this makes e inherent to any sort of equations that relate to growth/decay where the growth/decay is continuous (eg radioactive decay/bacterial growth) rather than calculated incrementally (eg compound interest calculated monthly)
It also crops up in more complex and less intuitive applications, like the solutions to differential equations.
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