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Consider the graph of   and sketch the graph of ...
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):
Consider the graph of   and sketch the graph of ...
Solve each of the following ...
Solve each of the following ...
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.
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?

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Pre-Cal 40S Slides November 14, 2007

  • 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?