Check up Use the Exponential Growth and Decay

Check up Use the Exponential Growth and Decay

Check up Use the Exponential Growth and Decay model: A =A 0ekt 1) What value in the model will show exponential growth? 2) Wat value in the model will show exponential decay? 3) If the model is graphed, what is the y intercept ? Check up 2 Solve the equation: 0.01t

335 =203.3e 4) Check up 4 Find the center and radius 2 2 5) x +2 + y - 4 =9

( ) ( ) Chapter 11 Section 1 Sequences and Summation Notation Page 822.

review Evaluate 3n + 1 for the values of n = 2, 4, 6 Definition Infinite Sequence: Notation: an a1 ,a2 ,a3 , . . . ,an , . . . { }

Function whose domain is the set of positive integers. Function values, or terms of the sequence: Finite Sequence: Domain consist only of the first n positive integers. Writing Terms of a Sequence from the General Form Write the first four terms of the sequence: an =3n +4 Solution: Term 1, n = 1 so a1 =3 1 +4

a1 =7 () () Term 2, n = 2 so a2 =3 2 +4 Try Find the first four terms of the sequence:

an - 1) ( = n n

3 -1 Factorial Notation n is a positive integer, notation n! (read n factorial) Product of all positive integers from n down through 1 n! = n(n 1)(n 2). . . (3)(2)(1) 0! (zero factorial), by definition, is 1. 0! = 1

Example 5! = (5)(4)(3)(2)(1) 23! = 2(3)(2)(1) Try Simplify 1) 4! 6! 2)

5! Find the first four terms 2n an = n- 1 ! (

) Summation Notation Notation for the sum of the first 7 terms in a sequence. a1 +a2 +a3 +a4 +a5 +a6 +a7 compact form: Summation Notation 7 ai

i=1 Read: the sum as i goes from 1 to 7 of ai i is the index of summation Symbol, (uppercase Greek letter sigma) as an instruction to add Summation Notation Sum of a sequence is represented by the summation notation. n

a i index of summation i=1 n upper limit of summation 1 lower limit of summation i Example Expand and evaluate

6 ( i=1 i2 +1 )

Solution: i goes from 1 to 6 so i=1 i=2 i=3 i=4 i =5 i=6 (1 + 1) + (4 + 1) + (9 + 1) + (16 + 1) + ((25 + 1) + (36 + 1)

Expand and evaluate 6 a) 2i i=1 5

b) 2 ( k=3 ) 2k - 3

Write in Summation Notation 3 3 3 3

a) 1 +2 +3 + . . . +7 1 1 1 1 b) 1+ + + + . . . + n- 1 3 9 27 3 Summary Infinite sequence

Finite sequence Writing term of a sequence Factorial Notation Summation Notation

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