7.1 Exploring Exponential Models p434. Repeated multiplication can be represented by an exponential function. It has the general form where ***x has D:

Slides:



Advertisements
Similar presentations
Compound interest & exponential growth/decay. Compound Interest A=P(1 + r ) nt n P - Initial principal r – annual rate expressed as a decimal n – compounded.
Advertisements

Exponential Growth Section 8.1. Exponential Function  f(x) = ab x where the base b is a positive number other than one.  Graph f(x) = 2 x  Note the.
Exponential Functions
Exponents and Properties Recall the definition of a r where r is a rational number: if then for appropriate values of m and n, For example,
Partner practice Chapter 8 Review WHITEBOA RD. Chapter 8 Review DRAW -The basic shape of the graph of a linear equation -The basic shape of the graph.
Graph each function: 1. f(x) = -2x 2 – 4x f(x) = -x 3 + 4x
Lesson 8.5 and 8.6 Objectives:
4-1 exponential functions, growth and decay
7-6 & 7-7 Exponential Functions
Objective: To identify and solve exponential functions.
Exponential Functions and Their Graphs Digital Lesson.
1. Given the function f(x) = 3e x :  a. Fill in the following table of values:  b. Sketch the graph of the function.  c. Describe its domain, range,
Lesson 6.2 Exponential Equations
From week#2 discussion on exponential functions. Populations tend to growth exponentially not linearly When an object cools (e.g., a pot of soup on the.
Exponential Growth Exponential Decay Graph the exponential function given by Example Graph the exponential function given by Solution x y, or f(x)
Exponential Growth & Decay
8-1 Exploring Exponent Models Objectives:  To identify exponential growth and decay.  To define the asymptote  To graph exponential functions  To find.
Exponents and Exponential Functions
8.2 – Properties of Exponential Functions
7.2 Compound Interest and Exponential Growth ©2001 by R. Villar All Rights Reserved.
Exploring Exponential Functions
Splash Screen. Lesson Menu Five-Minute Check (over Chapter 2) Then/Now New Vocabulary Key Concept:ExponentialKey Concept:Exponential FunctionFunction.
Exponential/logarithmic functions –word problems.
Sect 8.1 To model exponential growth and decay Section 8.2 To use e as a base and to apply the continuously and compounded interest formulas.
Graphing Exponentials and Logs
Chapter 8 Slide the Eraser. Question 1 write the following using exponents? 7 · 7 2 · 2 · 2 x · x · x· x · x· x · x.
7.1 Exponential Models Honors Algebra II. Exponential Growth: Graph.
Writing Exponential Growth Functions
EQ: How do exponential functions behave and why?.
Chapter 2: Functions and Models Lesson 4: Exponential Functions Mrs. Parziale.
Exponential Functions Learning Objective: to explore the graphs of exponential functions and the natural base. Warm-up (IN) 1.Complete the table. 2.Do.
Chapter 7 Exponential and Logarithmic Functions. 7-1, 7-2, and 7-3 Exponential Growth Exponential Decay The number “e”
Review: exponential growth and Decay functions. In this lesson, you will review how to write an exponential growth and decay function modeling a percent.
Objective Write and evaluate exponential expressions to model growth and decay situations.
7.1 –Exponential Functions An exponential function has the form y = ab x where a does not equal zero and the base b is a positive number other than 1.
MYTH You can’t fold a piece of paper in half more than 7 times.
Splash Screen. Then/Now You identified, graphed, and described several parent functions. (Lesson 1-5) Evaluate, analyze, and graph exponential functions.
Exponential Graphs Equations where the variable (x) is the POWER y = ab x – h + k h moves the graph horizontally k moves the graph vertically.
7-7 Simple and Compound Interest. Definitions Left side Principal Interest Interest rate Simple interest Right side When you first deposit money Money.
Do Now  Clickulators.. 60 Frankie took four tests and got an average score of 87.5%. If his fifth test raised his average to 90%, what was his.
Objectives:  Understand the exponential growth/decay function family.  Graph exponential growth/decay functions.  Use exponential functions to model.
5.2 Exponential Functions and Graphs. Graphing Calculator Exploration Graph in your calculator and sketch in your notebook: a) b) c) d)
Big Idea Compound Interest is the way most banks and other savings institutions pay savers who put their money into their accounts. Repeated Multiplication.
Exponential Functions Exponential Growth Exponential Decay y x.
Chapter 4.2 Exponential Functions. Exponents and Properties Recall the definition of a r, where r is a rational number: then for appropriate values of.
Exponential Growth and Decay Formula:
Exponential Functions,
7.2 Properties of Exponential Functions
8.1 & 8.2 Exponential Functions 3/10/2014. In this lesson we will learn … What an exponential function is. Difference between exponential growth and decay.
A function of the form: y = ab x where a ≢ 0, b > 0, and b ≢ 1 It is a nonlinear function. Exponential Growth (8.5) y = ab x where a>0 and b>1 (rises.
7-1 Exponential Functions
Exponential Growth and Decay. M & M Lab Part 1- Growth What happened to the number of M&Ms? Part 2-Decay What happened to the number of M&Ms? Increased.
8.1 Exploring Exponential Models
Graphing Exponential Functions Four exponential functions have been graphed. Compare the graphs of functions where b > 1 to those where b < 1.
HW: pg ,10,14,26-28 Do Now: Take out your pencil, notebook, and calculator. 1) Objectives: You will be able to define exponential functions. You.
Topic 6: Exponential Functions. Exploring Exponential Models.
Section 11-2 Graphs of Exponential Functions Objective: Students will be able to 1. Graph exponential functions and inequalities 2.Solve real life problems.
Holt Geometry 3-1 Lines and Angles A-SSE.A.1bInterpret expressions that represent a quantity in terms of its context. Interpret complicated expressions.
Drill If a quantity increases by the same proportion r in each unit of time, then the quantity displays exponential growth and can be modeled by the.
Chapter 7 Exponential and Logarithmic Functions. 7-1 Exponential Growth.
Warm Up Solve 9 2x = – Base e and Natural Logarithms.
Do Now #5 You decide to start a savings. You start with 100 dollars and every month you add 50% of what was previously there. How much will you have in.
EXPONENTIAL FUNCTIONS A BRIEF OVERVIEW. EXPONENTIAL FUNCTIONS.
Chapter 7 – Exponential and logarithmic functions
7.1 – Exploring Exponential Models
Exploring Exponential Models.
Warm up Express the following in simplest form: 7 − −3
6.1 Exponential Growth and Decay Functions
Exploring Exponential Models.
6.1 Exponential Growth and Decay Functions
Presentation transcript:

7.1 Exploring Exponential Models p434

Repeated multiplication can be represented by an exponential function. It has the general form where ***x has D: all real numbers

Ex 1) Graph

Ex) Determine if the function represents exponential growth or decay. State the y-intercept and the asymptote.

Note that b=1+r. The value b is called the growth or decay factor. The value r is called the growth or decay rate and is usually a percentage represented by a decimal.

Ex) You invested $1000 in a savings account at the end of the 6 th grade. The account pays 5% annual interest. How much money will be in the account after six years?

Ex) Suppose you invest $1000 in a savings Account that pays 5% annual interest. If you make no additional deposits or withdrawals, how many years will it take for the account to grow to at least $1500?

To model a discrete situation with an exponential model, you need to find b. If you know y –values for two consecutive x-values, you can find the rate of change using the formula and then b=1+r.

Ex) The table shows the world population of the Iberian lynx in 2003 and If this trend continues and the population is decreasing exponentially, how many Iberian lynx will there be in 2014?