1. 8.3 The natural base e

2. Definition of e
e 

3. The Graph of the Natural Base Function y = aex-h + k
Graph Natural base function.tii

4. The Graph of the Natural Base Function y = aex-h + k
Exponential function Natural base function
This function is an exponential
function.
* a changes the distance from the asymptote to the y-intercept.
h shifts the graph horizontally.
k shifts the graph vertically.
The a, h, k function the same.

5. The Graph of the Natural Base Function y = aex-h + k
Exponential function Natural base function
Exponential growth,
b > 1 ( With a positive x.)
* Exponential growth, e is greater than one with a positive x.
* Exponential decay b is greater than 0 but less than one. (With a positive x.)
* e is fixed so multiplying x by a negative number produces a decay.

6. Problems - Simplifying

7. Compound Interest Problem
Recall for the compound interest formula for interest compounded n times a year.
For continuous compounded (compounded all the time) we use the following formula.
A = balance P = principle r = %/100 t = years

8. Interest Problem
You deposit $975 in an account that pays 5.5% annual interest compounded continuously. What is the balance after 6 years?