Intro to Exponential Functions

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Intro to Exponential Functions

• Lesson 3.1

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Contrast
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Contrast

• Suppose you have a choice of two different jobs
  at graduation
• Start at 30,000 with a 6 per year increase
• Start at 40,000 with 1200 per year raise
• Which should you choose?
• One is linear growth
• One is exponential growth

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Which Job?

• How do we get each nextvalue for Option A?
• When is Option A better?
• When is Option B better?
• Rate of increase a constant 1200
• Rate of increase changing
• Percent of increase is a constant
• Ratio of successive years is 1.06

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Example

• Consider a savings account with compounded yearly
  income
• You have 100 in the account
• You receive 5 annual interest

View completed table
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Compounded Interest

• Completed table

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Compounded Interest

• Table of results from calculator
• Set y screen y1(x)1001.05x
• Choose Table (Diamond Y)
• Graph of results

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Exponential Modeling

• Population growth often modeled by exponential
  function
• Half life of radioactive materials modeled by
  exponential function

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Growth Factor

• Recall formula new balance old balance 0.05
  old balance
• Another way of writing the formula new balance
  1.05 old balance
• Why equivalent?
• Growth factor 1 interest rate as a fraction

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Decreasing Exponentials

• Consider a medication
• Patient takes 100 mg
• Once it is taken, body filters medication out
  over period of time
• Suppose it removes 15 of what is present in the
  blood stream every hour

Fill in the rest of the table
What is the growth factor?
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Decreasing Exponentials

• Completed chart
• Graph

Growth Factor 0.85 Note when growth factor lt
1, exponential is a decreasing function
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Solving Exponential Equations Graphically

• For our medication example when does the amount
  of medication amount to less than 5 mg
• Graph the functionfor 0 lt t lt 25
• Use the graph todetermine when

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General Formula

• All exponential functions have the general
  format
• Where
• A initial value
• B growth factor
• t number of time periods

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Typical Exponential Graphs

• When B gt 1
• When B lt 1

View results of Bgt1, Blt1 with spreadsheet
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Assignment

• Lesson 3.1A
• Page 112
• Exercises1 23 odd
• Lesson 3.1B
• Pg 113
• Exercises25 37 odd