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Intro to Exponential Functions

Intro to Exponential Functions

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Intro to Exponential Functions

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  1. Intro to Exponential Functions Lesson 3.1

  2. Contrast View differences using spreadsheet

  3. 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

  4. 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

  5. Example • Consider a savings account with compounded yearly income • You have $100 in the account • You receive 5% annual interest View completed table

  6. Compounded Interest • Completed table

  7. Compounded Interest • Table of results from calculator • Set y= screen y1(x)=100*1.05^x • Choose Table (Diamond Y) • Graph of results

  8. Exponential Modeling • Population growth often modeled by exponential function • Half life of radioactive materials modeled by exponential function

  9. Growth Factor • Recall formulanew balance = old balance + 0.05 * old balance • Another way of writing the formulanew balance = 1.05 * old balance • Why equivalent? • Growth factor: 1 + interest rate as a fraction

  10. 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?

  11. Decreasing Exponentials • Completed chart • Graph Growth Factor = 0.85 Note: when growth factor < 1, exponential is a decreasing function

  12. Solving Exponential Equations Graphically • For our medication example when does the amount of medication amount to less than 5 mg • Graph the functionfor 0 < t < 25 • Use the graph todetermine when

  13. General Formula • All exponential functions have the general format: • Where • A = initial value • B = growth factor • t = number of time periods

  14. Typical Exponential Graphs • When B > 1 • When B < 1 View results of B>1, B<1 with spreadsheet

  15. Assignment • Lesson 3.1A • Page 112 • Exercises1 – 23 odd • Lesson 3.1B • Pg 113 • Exercises25 – 37 odd