Exponential & Log Functions - Exercise 3 - Showing That Continuous Compounding is Exponential Growth

Show that when you compound interest instantly (n approaches infinity), that the resulting formula is

To do this, let m = n/r so 1/m = r/n. Replace r/n with 1/m. This also implies that n = mr so replace nt with mrt. Then use the definition of e and use the fact that if n approaches infinity, m also approaches infinity.

Also answer in your own words: What things in the natural world grow with continuously compounded growth as opposed to growth at the end of each fixed time period?

The Justification Has Been Provided - No Other Justification is Needed

STATEMENT	JUSTIFICATION
Let m = n/r r/n  = 1/m nt = mrt,  m approaches infinity	Given       Given     Substitution of Variables Definition of e