Question

Exponential growth
the formulas for growth
y=a(1+r)^x and y=a(e^kx)
where
y=result
a=starting amt.
r=rate
x=time elapsed
k=constant
any explanation when to use one of these???

Answer 1

these are identical if k = ln(1+r) in the second form ..... because exp(ln(1+r)) = (1+r).

IOW, they should give identical results.

the second form might be easier to do calculus with. the first might be easier to bung in a spreadsheet if you are using discrete time periods, eg compounding interest over months or quarters.

what is really interesting that that lim r --> infinity of (1+r)^(1/r) = e. that is at the heart of why both forms work, and is the basis of the actual calculation of e itself.

Answer 2

but their answers aren't identical