How do you approach a problem like this ?
GIVEN
f[x] = a E^(r x)
Calculate in terms of r the instantaneous growth rate of f[x] at any point x.
Do they mean work out the derivative, and then re-arrange for r= ?

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Im guessing a chain rule is applied here somehow

yep its asking for the derivative
instantaneous growth of (anything) would be like
d(anything) / dt

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