Calculus Sections 5.1 Apply exponential functions An exponential function takes the form y = a∙b x where b is the base and b>0 and b≠1. Identify as exponential.

Slides:



Advertisements
Similar presentations
6.6 The Natural Base, e.
Advertisements

Exponential Functions o Work on Exploration 1: Exponential Functions page 22 o Definition of Exponential Function o Graphs of Exponential Growth & Decay.
E. Exponential Growth or Decay? Growth Decay Growth.
8-6 Compound Interest and Exponential Growth
4-1:Exponential Growth and Decay
1 CALCULUS Even more graphing problems
Applied Calculus, 3/E by Deborah Hughes-Hallet Copyright 2006 by John Wiley & Sons. All rights reserved. Section 10.4 : Exponential Growth and Decay Section.
Continuous Growth and the Number e Lesson 3.4. Compounding Multiple Times Per Year Given the following formula for compounding  P = initial investment.
EXAMPLE 4 Classify and write rules for functions SOLUTION The graph represents exponential growth (y = ab x where b > 1). The y- intercept is 10, so a.
8.2 Day 2 Compound Interest if compounding occurs in different intervals. A = P ( 1 + r/n) nt Examples of Intervals: Annually, Bi-Annually, Quarterly,
SECTION Growth and Decay. Growth and Decay Model 1) Find the equation for y given.
Exponential Growth and Decay
8.3 The number e p. 480 What is the Euler number? How is it defined? Do laws of exponents apply to “e” number? How do you use “e” on your calculator? When.
Exponential Functions. Exponential Function f(x) = a x for any positive number a other than one.
AP Calculus Ms. Battaglia. Solve the differential equation.
The Natural Base e Section 6.2 beginning on page 304.
Section 6.3 Compound Interest and Continuous Growth.
8-1 Exploring Exponent Models Objectives:  To identify exponential growth and decay.  To define the asymptote  To graph exponential functions  To find.
Section 6.3 – Exponential Functions Laws of Exponents If s, t, a, and b are real numbers where a > 0 and b > 0, then: Definition: “a” is a positive real.
Section 7.1: Graph Exponential Growth Functions Chapter 7: Exponential and Logarithmic Functions.
Chapter 1.3 Exponential Functions. Exponential function F(x) = a x The domain of f(x) = a x is (-∞, ∞) The range of f(x) = a x is (0, ∞)
Essential Question: How do you find a growth factor and a decay factor?
Exponential Functions Section 1.3. Exponential Functions f(x) = a x Example: y 1 = 2 x y 2 = 3 x y 3 = 5 x For what values of x is 2 x
Compound Interest and Exponential Functions
Journal: Write an exponential growth equation using the natural base with a horizontal asymptote of y=-2.
Applications of Logs and Exponentials Section 3-4.
Exponential Functions Exponential Growth Exponential Decay Created by: David W. Cummins.
7.1 Exponential Models Honors Algebra II. Exponential Growth: Graph.
THE NATURAL BASE EXAMPLE 1 Simplify natural base expressions Simplify the expression. a.e2e2 e5e5 = e = e7e7 b. 12e4e4 3e3e3 = e 4 – 3 4 = 4e4e.
Chapter 11 Section 11.1 – 11.7 Review. Chapter 11.1 – 11.4 Pretest Evaluate each expression 1. (⅔) -4 = ___________2. (27) - ⅔ = __________ 3. (3x 2 y.
Exponential and Logistic Functions. Quick Review.
Exponential Functions and Their Graphs
Exponential Functions and Their Graphs Digital Lesson.
Real Exponents Chapter 11 Section 1. 2 of 19 Pre-Calculus Chapter 11 Sections 1 & 2 Scientific Notation A number is in scientific notation when it is.
Section 8 – 7 Exponential Functions Objectives: To evaluate exponential functions To graph exponential functions.
Logs Midterm Review Pre-Calculus. Topic 1: Be able to change logarithmic and exponential forms.
The Number e Section 8.3. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.
3.1 (part 2) Compound Interest & e Functions I.. Compound Interest: A = P ( 1 + r / n ) nt A = Account balance after time has passed. P = Principal: $
Pre-calc w-up 4/22 1.Graph y = 2 x+1 2.Graph y < 2 x – 1 For #3-4 Without graphing, describe how the graphs are related. 3.y = 4 x and y = 4 x – 3 4.y.
$100 $200 $300 $400 $500 $200 $300 $400 $500 Exponents Scientific Notation Exponential Growth and Decay Properties of exponents Geometry Sequences.
Growth and Decay: Integral Exponents
7.4 B – Applying calculus to Exponentials. Big Idea This section does not actually require calculus. You will learn a couple of formulas to model exponential.
9x – 7i > 3(3x – 7u) 9x – 7i > 9x – 21u – 7i > – 21u
Notes Over 8.2 Recognizing Exponential Growth and Decay Exponential Growth Model Exponential Decay Model.
Exponential Functions and Their Graphs Digital Lesson.
1.3 Exponential Functions. Interest If $100 is invested for 4 years at 5.5% interest compounded annually, find the ending amount. This is an example of.
Compound Interest Amount invested = £1000 Interest Rate = 5% Interest at end of Year 1= 5% of £1000 = 0.05 x  £1000 = £50 Amount at end of Year 1= £1050.
Essential Skills: Solve problems involving exponential growth Solve problems involving exponential decay.
4.4 Graph Exponential Growth Functions
Solve by Factoring Zero Product Property.
Section 5.5 Exponential Functions and Investing Copyright ©2013 Pearson Education, Inc.
EXPONENTIAL FUNCTIONS Section TOPIC FOCUS I can… Identify exponential growth and decay Graph exponential functions.
Graphing Exponential Growth and Decay. An exponential function has the form b is a positive number other than 1. If b is greater than 1 Is called an exponential.
8.5 and 8.6 Writing and Graphing Exponential Growth and Decay Functions Students will learn to Write exponential growth and decay functions Graph exponential.
Thurs 2/4 Lesson 7 – 1 Learning Objective: To graph exponential functions & solve interest problems Hw: Pg. 439 #10-25 all.
M 112 Short Course in Calculus Chapter 1 – Functions and Change Sections 1.7 – Exponential Growth and Decay V. J. Motto.
Do Now: State the domain of the function.. Academy Algebra II 7.1, 7.2: Graph Exponential Growth and Decay Functions HW: p.482 (6, 10, even), p.489.
6.2 Exponential Functions Notes Linear, Quadratic, or Exponential? Exponential Growth or Decay? Match Graphs Calculate compound Interest.
Calculus Section 5.3 Differentiate exponential functions If f(x) = e x then f’(x) = e x f(x) = x 3 e x y= √(e x – x) Examples. Find the derivative. y =
The Natural Base e An irrational number, symbolized by the letter e, appears as the base in many applied exponential functions. This irrational number.
Section 3.4 Continuous Growth and the Number e. Let’s say you just won $1000 that you would like to invest. You have the choice of three different accounts:
INVERSE Logarithmic and Exponential Graphs and Graphing.
Section 8-2 Properties of Exponential Functions. Asymptote Is a line that a graph approaches as x or y increases in absolute value.
Obj: Evaluate and graph exponential functions. Use compound formulas. Warm up 1.Find the limit. x ,00050,000100,000150,000 y.
Algebra II 8-1 (2). Starter: Graph: y = 2(4) x+3 -2 Asymptote: Domain: Range:
Exponential Functions Chapter5Section1. Exponential Functions Depending on the form of the base, b an exponential function can model growth (b>1) or decay.
Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Evaluate natural exponential and natural logarithmic functions. Model exponential.
AP Calculus AB Day 4 Section 6.2 9/14/2018 Perkins.
Algebra 1 Section 8.5 Apply Exponential Functions
Exponential Growth & Decay
Presentation transcript:

Calculus Sections 5.1 Apply exponential functions An exponential function takes the form y = a∙b x where b is the base and b>0 and b≠1. Identify as exponential growth, decay or neither. y = 3(1/2) x y = -5(3) x y = 6(-2) x

Graph the following functions y= 2 x y = 9∙3 -x

Graph the following functions y= e x y = e x+1 + 2

Continuous Compounding A = Pe rt You invest $12,000 at 6% interest rate compounded continuously for 5 years. What is its final value?

assignment Page 258 Problems 2-14 even, 28,30,32