Applications!!! DO NOT EAT THE M&M’s YET!!!.

Slides:

Advertisements

Similar presentations

Section 6.7 – Financial Models

Advertisements

Exponential Functions Functions that have the exponent as the variable.

6.2 Growth and Decay Law of Exponential Growth and Decay C = initial value k = constant of proportionality if k > 0, exponential growth occurs if k < 0,

 SOLVE APPLIED PROBLEMS INVOLVING EXPONENTIAL GROWTH AND DECAY.  SOLVE APPLIED PROBLEMS INVOLVING COMPOUND INTEREST. Copyright © 2012 Pearson Education,

ACTIVITY 40 Modeling with Exponential (Section 5.5, pp ) and Logarithmic Functions.

Unit 5 x y 20 x y 20 x y 20 x y 20 Check this = 10(1.1) 0 = 10(1+.1) = 10(1.1) 1 = 10(1+.1) 1.

Section 5.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models.

4_1 Day 2 The natural base: e.. WARM-UP: Graph (5/3)^x (5/3)^-x -(5/3)^x (5/3) ^x (5/3)^(x-2)

3.3 – Applications: Uninhibited and Limited Growth Models

OBJECTIVES: FIND EQUATIONS OF POPULATION THAT OBEY THE LAW OF UNINHIBITED GROWTH AND DECAY USE LOGISTIC MODELS Exponential Growth and Decay; Logistic Models.

1.3 Exponential Functions Acadia National Park, Maine.

Precalc. 2. Simplify 3. Simplify 4. Simplify.

1.3 Exponential Functions Mt. St. Helens, Washington State Greg Kelly, Hanford High School, Richland, Washington.

SECTION Growth and Decay. Growth and Decay Model 1) Find the equation for y given.

Exponential Functions and Their Graphs Digital Lesson.

Exponential Growth & Decay Modeling Data Objectives –Model exponential growth & decay –Model data with exponential & logarithmic functions. 1.

Exponential Functions An exponential function is a function of the form the real constant a is called the base, and the independent variable x may assume.

CHAPTER 1: PREREQUISITES FOR CALCULUS SECTION 1.3: EXPONENTIAL FUNCTIONS AP CALCULUS AB.

Section 1.2 Exponential Functions

Exponential Functions. Exponential Function f(x) = a x for any positive number a other than one.

Exponential Growth & Decay, Half-life, Compound Interest

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,

10.7 Exponential Growth and Decay

Quiz 3-1a This data can be modeled using an exponential equation 

Exponential and Logarithmic Functions

Chapter 3 Exponential and Logarithmic Functions

Section 6.4 Solving Logarithmic and Exponential Equations

1.3 Exponential Functions Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2004 Yosemite National Park, CA.

8.2 – Properties of Exponential Functions

7.2 Compound Interest and Exponential Growth ©2001 by R. Villar All Rights Reserved.

Applications and Models: Growth and Decay

Exponential Functions

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.

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.

Quiz 3-1a 1.Write the equation that models the data under the column labeled g(x). 2. Write the equation that models the data under the column labeled.

Section 4.2 Logarithms and Exponential Models. The half-life of a substance is the amount of time it takes for a decreasing exponential function to decay.

Answers to even-numbered HW problems Section 4.2 S-8 Yes, it shows exponential growth because x values are evenly spaced and ratios of successive y values.

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.

Exponential Modeling Section 3.2a.

Objectives: Determine the Future Value of a Lump Sum of Money Determine the Present Value of a Lump Sum of Money Determine the Time required to Double.

Objectives:  Understand the exponential growth/decay function family.  Graph exponential growth/decay functions.  Use exponential functions to model.

Exponential Functions and Their Graphs/ Compound Interest 2015/16.

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.

Growth and Decay Exponential Models.

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.

Exponential Growth and Decay Word Problems

Section 6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models.

Section 3.5 Exponential and Logarithmic Models. Compound Interest The compound interest formula: A is the amount in the account after t years. P is the.

Exponential Growth and Decay 6.4. Slide 6- 2 Quick Review.

Warm-up Identify if the function is Exp. Growth or Decay 1) 2) Which are exponential expressions? 3)4) 5)6)

Section 5.6 Applications and Models: Growth and Decay; and Compound Interest Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

7.3B Applications of Solving Exponential Equations

MAT 150 Module 8 – Exponential Functions Lesson 1 – Exponential functions and their applications.

7.2 Properties of Exponential Functions

Modeling Constant Rate of Growth (Rate of Decay) What is the difference between and An exponential function in x is a function that can be written in the.

Constant Rate Exponential Population Model Date: 3.2 Exponential and Logistic Modeling (3.2) Find the growth or decay rates: r = (1 + r) 1.35% growth If.

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:

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.

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.

Copyright © 2012 Pearson Education, Inc. Publishing as Addison Wesley CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential.

E XPONENTIAL W ORD P ROBLEMS Unit 3 Day 5. D O -N OW.

* 1. * 2.. * Review the P.O.T.D. * Review compounding continuously * Exponential and e word problems.

3.5 Exponential and Logarithmic Models n compoundings per yearContinuous Compounding.

Applications of Exponential Functions

1.3 Exponential Functions Day 1

AP Calculus AB Day 4 Section 6.2 9/14/2018 Perkins.

Exponential Functions and Their Graphs

Exponential Functions

1.3 Exponential Functions

Presentation transcript:

Applications!!! DO NOT EAT THE M&M’s YET!!!

Exponential Regression. Enter data: STAT button/EDIT column/EDIT function Enter turn data into L1/enter M&M’s data into L2 2 nd button/MODE button Regression STAT button/CALC column/0 or ExpReg function Type L1, L2 Enter Y = a(b) x where a = __________/ b = _________ Does a equal your initial starting value? Why? Is this a half-life scenario? Why/Why not?

Growth & Decay Ex.#2 Let y represent the mass of a particular radioactive element whose half-life is 25 years. After t years, the mass in grams is given by. a.What is the initial mass (when t = 0)? b.How much of the element is present after 80 years?

Growth & Decay Ex.#2 Let y represent the mass of a particular radioactive element whose half-life is 25 years. After t years, the mass in grams is given by. a.What is the initial mass (when t = 0)? b.How much of the element is present after 80 years? So points on the graph: Let m 0 = initial mass m 80 = mass after 80 yrs Points on graph (25, m 0 /2 ) (0, m 0 ) (80, m 0 )

Growth & Decay Ex.#3 Let y represent the mass of a particular radioactive element. After t years, the mass in grams is given by. a.What is the initial mass (when t = 0)? b.After 20 years there are 15 grams of the element left; what is the half life?

Compound Interest—Ex 1. The “easier questions” A __________ investment is made into a ____________ fund at a rate of ____. Compounded __________. Question: After ______ years how much money was in the account?

Compound Interest—Ex 2. Time to double of triple.. A investment is made into a ____________ fund at a rate of ____. Question: How long will it take for the investment to ________ in value?

Compound Interest—Ex 3. Find the rate… A investment is made into a ____________ fund at a rate of ____. Compounded __________. The balance after ___ years is _________. Question: What is the annual percentage rate?

Logistic Growth Models

H.W.: p. 327(30, 32, 33, 34, 36, 46, 63) Ditto Section 4.4