1. Algebra 1 Warm Up 4,5 April 2012 Find the constant multiplier for each sequence, then find the next 3 terms 1) 16, 24, 36, ___, ___, ___ 2) 100,80,64, ___, ___, ___ 3) 1000,1200,1440, ___, ___, ___ Explain how you can find the constant multiplier and use it to find the next terms using words. Homework due Friday: pg. 337: 1- 4 all, 6

2. OBJECTIVE Today we will explore exponential growth and decay patterns and write exponential equations. Today we will take notes, work problems with our groups and present to the class.

3. Once upon a time, two merchants were trying to work out a deal. For the next month, the 1 st merchant was going to give $10,000 to the 2 nd merchant, and in return, he would receive 1 cent the first day, 2 cents the second, 4 cents in the third, and so on, each time doubling the amount. After 1 month, who came out ahead?

4. 7) Percent increase or decrease. a) Starting value: 16, Increases by 50% each term b) how? Multiply the term by 0.50 and ADD that amount to the previous term c) what is the constant multiplier? 16, ___?? 16 x 0.50 = 8 16 + 16(.50) = 16 + 8 = 24 24 x 0.50 = 12 24 + 24(.50) = 24 +12 = 36 36 what are the next three terms?? 24

5. Finish Handout 6.1 Do # 3 and 4 Finished? Do # 5 Be ready to share your work with the class.

6. words to know recursive routine: a starting value and a recursive rule for generating a sequence. You apply the rule to the starting value, then keep applying the rule to the resulting value to get the next value. recursive– repeating the rule over and over to get the next term based on the previous term

7. bugs, bugs, bugs Imagine a bug population invaded your classroom. One day you notice 16 bugs. Every day, new bugs hatch, increasing the population by 50% every week. So in the first week, the population increases by ½ of 16 or increases by 8. The new population is 16 + 8 = 24.

8. CW: Pg. 333 Complete the investigation and graph Weeks elapsed Increase in # of bugs Total number of bugs Ratioratio as a decimal start (0) 16 1 2 3 4 GRAPH: let x represent the number of weeks elapsed and y represent the total number of bugs

9. Exponential Growth & Decay Applications that Apply to Me! A B

10. CW: Consider the table xy 010 120 240 380 4160 5 What is the starting value? What is the constant multiplier? Can you use these two number to find an equation? 10 2

11. EXPONENTIAL FUNCTIONS EXPONENTIAL EQUATION (Functions) FINAL VALUE STARTING VALUE CONSTANT MULTIPLIER EXPONENT

12. EXPONENTIAL GROWTH AND DECAY Notice: The variable x is an exponent. As such, the graphs of these functions are not straight lines. In a straight line, the "rate of change" is the same across the graph. In these graphs, the "rate of change" increases or decreases across the graphs.

13. The graphs of exponential functions change based upon the values of a and b: when a > 0 and the b is between 0 and 1, the graph will be decreasing (decaying). For this example, each time x is increased by 1, y decreases to one half of its previous value. Such a situation is called Exponential Decay. when a > 0 and the b is greater than 1, the graph will be increasing (growing). For this example, each time x is increased by 1, y increases by a factor of 2. Such a situation is called Exponential Growth

14. debrief How does the exponential growth differ from linear growth? How does the difference show up in the table? How does the difference show up on the graph? True or false? The more bugs you start with, the more are added each week.