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

