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Overgrown Redwood Log and Wildflowers The Natural Logarithm ...

Pre-Cal 40S April 22, 2009

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More solving logarithmic equations and a gentle introduction to the number e.

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Page 1: Pre-Cal 40S April 22, 2009

Overgrown Redwood Log and Wildflowers

The Natural Logarithm ...

Page 2: Pre-Cal 40S April 22, 2009

Now lets solve some logarithmic equations ...

Page 3: Pre-Cal 40S April 22, 2009

Now lets solve some logarithmic equations ...

Page 4: Pre-Cal 40S April 22, 2009

And now, solve these logarithmic equations ...

Page 5: Pre-Cal 40S April 22, 2009

And now, solve these logarithmic equations ...

Page 6: Pre-Cal 40S April 22, 2009

And now, solve these logarithmic equations ...

Page 7: Pre-Cal 40S April 22, 2009

Properties of exponential functions

Properties of the exponential growth functionDomain: Range: Root(s): y-intercept: Increasing of Decreasing: Concavity: Asymptote(s):

For example, let's look ata > 1

Page 8: Pre-Cal 40S April 22, 2009

As an example let's look at

Domain: Range: Root(s): y-intercept: Increasing or Decreasing: Concavity: Asymptote(s):

0 < a < 1

Properties of exponential functions

Properties of the exponential decay function

Page 9: Pre-Cal 40S April 22, 2009

Properties of logarithmic functions

Properties of the logarithmic growth functionDomain: Range: Root(s): y-intercept: Increasing of Decreasing: Concavity: Asymptote(s):

For example, let's look ata > 0, a ≠ 1

Page 10: Pre-Cal 40S April 22, 2009

As an example we'll look at0 < a < 1

Properties of logarithmic functions

Properties of the logarithmic decay functionDomain: Range: Root(s): y-intercept: Increasing of Decreasing: Concavity: Asymptote(s):

Page 11: Pre-Cal 40S April 22, 2009

Who wants to be a millionaire?

What is compound interest?How does this formula "work"?

How much money will you have after 5 years if you invest $300.00 at 6% interest compounded annually? monthly?