Warm-Up 1. Solve: 2. Solve: 3. Could side lengths of 12, 19, and 9 be used to create a right triangle?

Day 1: Now/Next (recursive) Equations Unit 3: Functions Day 1: Now/Next (recursive) Equations

The Rabbit Problem (Fibonacci’s Problem) CORE The Rabbit Problem (Fibonacci’s Problem) http://youtu.be/X1L8XMTi_Vw

Month 1 2 3 4 5 6 7 8 9 10 Pairs of Rabbits a. What pattern do you notice?     b. How many rabbits are there after 11 months have passed?     C. How many rabbits are there after 12 months have passed?     D. Write a rule to find out how many rabbits are in any given month, based on the number of rabbits from previous months. What is the START value

What you have created is called a Sequence A sequence a list of numbers where each term is based on the previous term or a combination of previous terms using a set pattern or rule. More specifically: A recursive equation is an equation that shows how to calculate the value of the next term in a sequence from the value of the current term (or a combination of previous terms)

Fibonacci Numbers http://www.youtube.com/watch?v=ahXIMUkSX X0&feature=related The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in Italian since he was born in Pisa,Italy, the city with the famous Leaning Tower, about 1175 AD

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Introducing the Decimal Number system into Europe He did not invent the Fibonnaci sequence but he wrote a book about the mathematicians who studied this sequence before him. It was the French mathematician Edouard Lucas (1842-1891) who gave the name Fibonacci numbers to this series

When writing a rule you must include: The start Value The Next/Now Equation

“Guess My Rule” – Back to sequences a) 5, 10, 15, 20, . . . START = 5, NEXT = NOW + 5 b) 2, 4, 8, 16, 32, . . . START = 2, NEXT = NOW•2

Term Value 1 52 2 46 3 40 4 34 5 28 Term Value 1 -3 2 6 3 -12 4 24 5 C. D. Term Value 1 -3 2 6 3 -12 4 24 5 -48 The term means the placement of that value. If the term is 1, it is the first value in that sequence.

Using the Calculator n = 1 n = 2 n = 3 n = 4 A = 1 A = 3 A = 5 A = 7 Use the calculator to create the term n = 10. Enter your initial value, then take advantage of the ANS key to create a function to iterate simply by pressing ENTER repeatedly. For example, to iterate NEXT = NOW + 2, starting at an initial value of 1: Hit 1, ENTER. Enter Ans+2 and then hit ENTER repeatedly. Calculators can quickly iterate functions

Use the calculator to create the table of the function : Next = 5Now + 10 Term Value 1 2 15 3 4 5 6 7

a)Write the function for the sequence: b) find the 10th term of the sequence P = 3 n = 2 P = 4 n = 3 P = 5 n = 4 P = 6

a)Write the function for the a)Write the function for the sequence: b) find the 10th term of the sequence n = 1 P = 4 n = 2 P = 8 n = 3 P = 12 n = 4 P = 16

n = 1 A = 1 n = 2 A = 3 n = 3 A = 5 n = 4 A = 7 a)Write the function for the sequence: b) find the 10th term of the sequence

On the lined side of the index card: Create a sequence that can be represented by a next/now function. Give at least 4 terms in your sequence. Write your name on the lined side of the index card.

Find a partner NOT at your table. Write the partners name on the white side of the index card. Have your partner create the now/next function for your sequence. Partners turn in the index card to the bin at the front of the room.

HW. 3.1