Working with The Exponential and natural log functions. Introduction to exponential modeling.

1. Consider the graph of and sketch the graph of ...

2. Properties of The Exponential and Natural Log Functions
Let's compare
Properties of The
Properties of The
Natural Log Function
Exponential Function
Domain:
Domain:
Range:
Range:
Root(s):
Root(s):
y-intercept:
y-intercept:
Increasing of Decreasing:
Increasing of Decreasing:
Concavity:
Concavity:
Asymptote(s):
Asymptote(s):

3. Consider the graph of and sketch the graph of ...

4. Solve each of the following ...

5. Solve each of the following ...

6. Exponential Modeling
The basic function:
How we model real life situations depends on what kind, or how much ,
information we are given:
Case 1: Working with a minimal amount of information (A,Ao, ∆t).
We will create a model in base 10 and base e ... base e is prefered.
is the original amount of quot;substancequot; at the
beginning of the time period.
A is the amount of quot;substancequot; as the end of the time
period.
Model is our model for the growth (or decay) of the
substancequot;, it is usually an exponential expression in
base 10 or base e although any base can be used.
t is the amount of time that has passed for the
substancequot; to grow(or Decay) from to A.

7. Example: The population of the earth was 5 billion in 1990. In 200l it was
6.2 billion.
(a) Model the population growth using an exponential function.
(b) What was the population in 1999?