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Unit 3 Day 5 – Exponential Growth and Decay

Unit 3 Day 5 – Exponential Growth and Decay. Warm-Up 1. Vote: Would you rather have your midterm on Wednesday or Thursday? Please pick only one day or you will forfeit your vote. 2. How do you think you did on Unit 3A? What can you do differently for unit 3B?. Intro . ZOMBIES!

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Unit 3 Day 5 – Exponential Growth and Decay

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  1. Unit 3 Day 5 – Exponential Growth and Decay

  2. Warm-Up 1 • Vote: Would you rather have your midterm on Wednesday or Thursday? Please pick only one day or you will forfeit your vote. 2. How do you think you did on Unit 3A? What can you do differently for unit 3B?

  3. Intro ZOMBIES! A rabid pack of zombies is growing exponentially! After an hour, the original zombie infected 5 people total, and those 5 zombies went on to infect 5 people, etc. After a zombie bite, it takes an hour to infect others. Develop a plan to determine how many newly infected zombies will be created after 4 hours. If possible, draw a diagram, create a table, a graph, and an equation.

  4. Essential Questions How can exponential functions model real-world problems and solutions?

  5. Review of Vocabulary • Initial Value: The first term in a sequence or the dependent value associated with an independent value of 0. • Common Ratio: The ratio of one term in a sequence and the previous term. (What you multiply by each time!) • Common Difference: The difference between one term in a sequence and the previous term. (What you add each time!)

  6. Recursive function: a function that can be used to find any term in a sequence if you have the previous term (i.e. NOW-NEXT) • Explicit function: a function that can be used to find any term in the sequence without having to know the previous term. (i.e. y = or f(x) = )

  7. Domain: the set of all input values for a function • Theoretical Domain: the set of all input values for a function without consideration for context • Practical Domain: the set of all input values for a function that are reasonable within context

  8. Investigation #1 Questions: • 1. What is your initial value for this set of data? What does it represent in the investigation? • 2. Would it make more sense to find a common ratio (r) or common difference (d) for this data? Explain. • 3. Based on your answer to Question 2, find the r OR d for the data you collected. Show the process you used to do so.

  9. Could you estimate your answer to Question 3 without conducting the exploration? If so, how? 5. Write a recursive (NOW-NEXT) function that would help you make predictions for this data. 6. Write an explicit function using function notation that would help you make predictions for this data. In your function let x be the stage of the investigation and let f(x) equal the number of people standing in that stage.

  10. Increasing by a specific number Ex, doubling, tripling, halving B = 2 3 ½ Recursive: Next = NOW ∙ b Explicit: Starting at a, y = abx

  11. If Growth/Decay is a PERCENTAGE!!! NEXT = NOW ∙ b Starting at a, y = abx

  12. Closure ZOMBIES!! • At 9:00 am, the official count of the zombie infestation was 16384. Every hour the number of zombies quadruples. Around what time did the first zombie roll into town? • There are 2 people infected and the rate of infection of new people is a growth rate of 15% every hour. How many people are infected in 6 hours?

  13. Homework • Independent practice

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