3 1 ASSE A 1 b Interpret expressions

3 -1 A-SSE. A. 1 b Interpret expressions that represent a quantity in terms Lines and Angles of its context. Interpret complicated expressions by viewing one or more of their arts as a single entity. A-CED. A. 2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. F-IF. C. 7 e Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Holt Geometry

Lines and Angles 3 -1 Ø Asymptote Ø Decay factor Ø Exponential decay Ø Exponential function Ø Exponential growth Ø Growth factor Holt Geometry

{ Paper for notes 3 -1 Lines and Angles { Graph paper { Pearson 7. 1 { Graphing Calc. Holt Geometry

TOPIC: 3 -1 Lines and Name: Daisy Basset Angles Period: Subject: 7. 1 Exploring Exponential Models Objective: Holt Geometry Notes Graph exponential functions. Date :

Vocabulary 3 -1 Lines and Angles Ø Exponential Function (draw the graph and labels) Ø Ø Ø Exponential Growth Exponential Decay Asymptote Growth Factor Decay Factor Holt Geometry

3 -1 Lines and Angles 1. Make a table of values and graph each. Holt Geometry

A. y = 2 3 -1 Lines and Angles x Holt Geometry x -4 -3 -2 -1 0 1 2 3 2 x y 2 -4 0. 0625 2 -3 0. 125 2 -2 0. 25 0. 5 2 -1 20 1 2 21 4 22 23 8

3 -1 Lines and Angles 2. Identify each function or situation as an example of exponential growth or decay. What is the y-intercept? Holt Geometry

A. y = a x 12(0. 95) 3 -1 Lines and Angles b Since, a>0 and 0<b<1 , the function represents exponential decay. Holt Geometry

y= x 12(0. 95) y= 0 12(0. 95) 3 -1 Lines and Angles y-intercept ( 0 , 12 ) Holt Geometry

B. y = x 0. 25(2) 3 -1 Lines and Angles a b Since, a > 0 and b > 1 , the function represents exponential growth. Holt Geometry

y= x 0. 25(2) y= 0 0. 25(2) 3 -1 Lines and Angles y-intercept (0, 0. 25 ) Holt Geometry

C. You put $1000 into a college savings account for 4 years. The account pays 5% interest annually. 3 -1 Lines and Angles Holt Geometry

The amount of money in the bank grows 5% annually. 3 -1 Lines and Angles It represents exponential growth. Holt Geometry

The y-intercept represents the amount of _____ money at time _______, = 0 which is the initial investment. 3 -1 Lines and Angles Holt Geometry

3 -1 Lines and Angles The y-intercept is $1000 , , which is the dollar value of the initial investment. Holt Geometry

$1000 in a savings 3 -1 Lines and Angles account at the end th of 6 grade. The account pays 5% annual interest. Holt Geometry

How much money will be in the account after six years? 3 -1 Lines and Angles A(t) = a(1 + Holt Geometry t r)

A(t) = a(1 + 3 -1 Lines and Angles t r) A(t) = Amt. after t time periods a = initial amount = $1000 r = rate of growth/decay = 5% = 0. 05 number of time periods = 6 t= Holt Geometry

A(t) = a(1 + 3 -1 Lines and Angles A(6) = 1000(1 + A(6) = t r) 6 0. 05) 6 1000(1. 05) A(6) ≈ $1340. 095641 The account contains $1340. 10 after 6 years. Holt Geometry

3 -1 Lines and Angles Summary D L I Q Holt Geometry Summarize/reflect What did I do? What did I learn? What did I find most interesting? What questions do I still have? What do I need clarified?

3 -1 Lines and Angles { Notes 7. 1 { Graphing Calc. Holt Geometry

4. Suppose you invest $500 in a savings account that pays 3. 5% annually. How much will be in the account after 5 years? 3 -1 Lines and Angles Holt Geometry

A(t) = a(1 + 3 -1 Lines and Angles t r) A(t) = Amt. after t time periods a = $500 r = 3. 5% = 0. 035 t= 5 Holt Geometry

A(t) = a(1 + 3 -1 Lines and Angles A(5) = 500(1 + A(5) = t r) 5 0. 035) 5 500(1. 035) A(5) ≈ $593. 8431528 The account contains $593. 84 after 5 years. Holt Geometry

5. Suppose you invest $1000 in a savings account that pays 5% annually. 3 -1 Lines and Angles Holt Geometry

If you make no additional deposits or withdrawals, how many years will it take for the account to grow to at least $1500? 3 -1 Lines and Angles Holt Geometry

A(t) = a(1 + 3 -1 Lines and Angles t r) A(t) = Amt. after t time periods a = $1000 r = 5% = 0. 05 t= ? Holt Geometry

A(t) = a(1 + 3 -1 Lines and Angles A(t) = 1000(1 + A(t) = t r) t 0. 05) t 1000(1. 05) Use the table on the calculator. Holt Geometry

3 -1 Lines and Angles The account will contain $1500 after 9 yrs. Holt Geometry

3 -1 Lines and Angles 6. Holt Geometry Suppose you invest $500 in a savings account that pays 3. 5% annually. When will the account contain $650?

A(t) = a(1 + 3 -1 Lines and Angles A(t) = 500(1 + A(t) = t r) t 0. 035) t 500(1. 035) Use the table on the calculator. Holt Geometry

3 -1 Lines and Angles The account will contain $650 after 8 years. Holt Geometry

3 -1 Lines and Angles Summary D L I Q Holt Geometry Summarize/reflect What did I do? What did I learn? What did I find most interesting? What questions do I still have? What do I need clarified?

3 -1 Lines and Angles 7. 1: Math XL Start Notes 7. 2 Work on the Study Plan Holt Geometry

TOPIC: Daisy Basset Angles 3 -1 Lines and. Name: Period: 7. 2 Properties of Exponential Functions Objective: Holt Geometry Date : Subject: Notes Graph exponential functions showing intercepts and end behavior.

Key Concept 3 -1 Lines and Angles Ø Parent Function Ø Stretch, Shrink, Reflection Holt Geometry