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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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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