Exponential and Logarithmic Function

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Exponential and Logarithmic Function

• Lesson 2.4

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Animated Exponential Function
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Exponential Function

• Definition
• Where
• b gt 0 is a constant
• b ? 1
• a is a constant

b lt 1
a
a
b gt 1
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Reminder

• Properties of exponents
• Note Theorem 2.8, pg 81
• Properties of exponential functions

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Example

• Consider equation
• Solution
• Note that calculatorwill solve also

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Logarithmic Functions

• Inverse of exponential functions
• Learn to translate back and forth from one form
  to the other

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Examples

• Try these

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Solutions

• Check your work

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Natural Log

• Often the number e ? 2.71828 is used as the base
  for logarithms logex ln x
• This is the inverse of the exponential function
  with e as the base
• Many computer languages use exp(x) for ex

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Changing Bases

• To change from base b to base a, use the formula
  shown

Hint base a will be base 10
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Using Logarithms

• Use to solve exponential equations

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Application of Exponents

• Exponential Growth
• y P0 ax periodic exponential growth
• y P0 ekt continuous exponential growth

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Application of Exponents

• Annually compounded interest A (1 r)t
• Compounded n times per year
• Continuous compounding A P ert

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Assignment

• Lesson 2.4
• Page 89
• Exercises 1 39 odd, 55 69 odd