1. e

2. Exponential Growth or Decay? Growth Decay Growth

3. Exponential Growth or Decay? We need to know what e is…. e is number discovered by Euler. e = 2.71828…. Like π it is irrational. So because e is greater than 1 this function would be an exponential growth.

4. Performing Mathematics with e Recall: Well, since e is just a number /base all of these rules apply for e

5. =8e 2

6. Graphing e e follows all the rules of exponential growth and decay. GrowthDecay f(x)= 2e x f(x)= 2e -x x

7. Growth Decay f(x)= 2e x f(x)= 2e -x x : none y : (0,2) D: (- ∞,∞) R: (0, ∞) Asy: y = 0 x : none y : (0,2) D: (- ∞,∞) R: (0, -∞) Asy: y = 0 x : none y : (0,2) D: (- ∞,∞) R: (0, ∞) Asy: y = 0 x : none y : (0,2) D: (- ∞,∞) R: (0, -∞) Asy: y = 0 x

8. Compounding Continuously A more accurate depiction of what happens in nature (and mutual funds!) A = final amount P = beginning amount r = interest rate NOT in % form t = time (years)