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1/4 Adv. Alg. Bell Ringer

1/4 Adv. Alg. Bell Ringer. Grab today’s handout and vocabulary Get out Test Analysis/NYR Sheet (handed in shortly) Answer question below: How much money would Sandy have if she invested $500 for 10 years at 12% annual interest? Recall, Amt = P(1+r) t.

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1/4 Adv. Alg. Bell Ringer

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  1. 1/4 Adv. Alg. Bell Ringer Grab today’s handout and vocabulary Get out Test Analysis/NYR Sheet (handed in shortly) Answer question below: How much money would Sandy have if she invested $500 for 10 years at 12% annual interest? Recall, Amt = P(1+r)t Homework: Finish Inverse Exponential/Logarithm Indep. Practice

  2. 1/4/11 News and Notes • Hand in Test Analysis/NYR Sheet • Reminder: Tomorrow after school to take test • Perfection Award Winner Day 1:

  3. 1/4 Agenda • I CAN create inverse table and graph of exponential function to introduce logarithmic functions, and understand the types of questions logarithms allow you to answer. • Bell Ringer • New Material – Vocab, 2 examples • Guided Practice – Inverse table and graph • Independent Practice

  4. New Material – Motivation • What if we want to find how long it would take for something to happen? • Example: Manny just got $500 for Christmas. How long would it take him to earn $10,000 if he invested his money at 12% annual interest? A = P(1+r)t 10,000 = 500(1.12)x 500 500 20 = 1.12x HOW DO WE SOLVE THIS!?

  5. How do we solve these? • 20 = 1.12x • Or what if I asked you how long it would take for our world’s population to get to 12,000,000,000 people if we grow at 4% per year? • Or what if I asked you how long it took for 1,000,000 Dodo Birds to become endangered (only 50 left) if their population declined at 13% per year? • What do you notice about the three equations? • WE HAVE TO SOLVE FOR THE EXPONENT OF THE EQUATION… • This requires the LOGARITHMIC FUNCTION

  6. VOCABULARY

  7. 2 Big Key Points • When are log functions useful? • When solving for the exponent of an exponential function. • What are log functions? • The inverse of an exponential function. • So let’s look at the inverse of an exponential function in a table and graph:

  8. Find the log function:

  9. Symmetrical across the line y=x

  10. Guided Practice • What type of function are we starting with? • Graph the above table, write the inverse table, graph the inverse, and then answer the question that follows.

  11. Questions to Consider • Question: What type of function is the inverse of the exponential function? • LOGARITHMIC FUNCTION

  12. Independent Practice • You now have the rest of class to work on the independent practice.

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