1. Natural Exponential Function

2. Natural Exponential Function
The base is e
e is an irrational number
Referred to as the exponential function

3. Graphing Natural Exponential Functions
Similar to graphing exponential functions
Create a table of values and graph the points
Find the horizontal asymptotes
Transformations occur the same way for natural exponential functions as exponential functions

4. Ex: graph f(x)=ex graph f(x)=e-xy -3
.049 -2
.135 -1
.368 1
2.718 2
7.389 3
20.086 x y -3
20.086 -2
7.389 -1
2.718 1
.368 2
.135 3
.049

5. Compound Interest Represented by a exponential function
A(t)=P(1+r/n)nt
A(t) is amount after t years
P is principal
R is interest rate (as a decimal)
n is number of times interest is compounded per year
t is number of years

6. Compounding Annual n=1 Semiannual n=2 Quarterly n=4 Monthly n=12
Daily n=365
Weekly n=52

7. Continuously Compounded Interest
Represented by a natural exponential function
Interest is being compounded every instant!
A(t)=Pert
A(t) is amount after t years
P is principal
r is interest rate (as a decimal)

8. Exponential Population Growth
n(t)=n0ert
“b” is e because we are being more specific for populations
n(t) is population at time t
n0 is initial size of the population
r is relative rate of growth
t is time

9. Exponential Population Growth
n(t)=n0ert
We can use this to:
Predict the size of a population
Compare effects of different rates of population growth
Find the initial population

10. Practice/Hw
p. 394 #1, 11-14
8.8
1-3 all
6-8 a,c