4.9 Exponential and Log/Ln Word Problems Example: Given that population is growing exponentially with the function (this is based on historical data from.

Slides:

Advertisements

Similar presentations

8.3 Radioactive Dating.

Advertisements

Copyright © 2009 Pearson Education, Inc. CHAPTER 5: Exponential and Logarithmic Functions 5.1 Inverse Functions 5.2 Exponential Functions and Graphs 5.3.

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

Exponential Growth and Decay

MATH 109 Exam 2 Review. Jeopardy Show Me The $$$$$ Potent Potables Famous Log Cabins Captain’s Log Potpourri

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.

Exponential Growth and Decay Models; Logistic Growth and Decay Models

Copyright © Cengage Learning. All rights reserved. 3 Exponential and Logarithmic Functions.

3 Exponential and Logarithmic Functions

Modeling with Exponential and Logarithmic Functions

5. 6. Further Applications and Modeling with

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

3.5 Exponential and Logarithmic Models -Students will use exponential growth and decay functions to model and solve real-life problems. -Use Gaussian functions.

Section 3.5 Exponential and Logarithmic Models. Important Vocabulary Bell-shaped curve The graph of a Gaussian model. Logistic curve A model for describing.

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

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 4 Inverse, Exponential, and Logarithmic Functions Copyright © 2013, 2009, 2005 Pearson Education,

Chapter 3 Exponential and Logarithmic Functions

Applications. Assignment Radioactive Dating – Uranium-235 is one of the radioactive elements used in estimating the age of rocks. The half life of U-235.

Exponential Growth and Decay 6.4. Exponential Decay Exponential Decay is very similar to Exponential Growth. The only difference in the model is that.

4.8 Exponential and Logarithmic Models

Rates of Growth & Decay. Example (1) - a The size of a colony of bacteria was 100 million at 12 am and 200 million at 3am. Assuming that the relative.

Rates of Growth & Decay. Example (1) The size of a colony of bacteria was 100 million at 12 am and 200 million at 3am. Assuming that the relative rate.

Applications and Models: Growth and Decay

#1. #2 #3 Graph by hand. #4 #5 If $5000 is invested at 9% interest, find the amount after three years if the interest is compounded (a) monthly.

7.2 Half-Life the time it takes for half of a radioactive sample to decay is a constant rate (always the same half life for each element) Example: Strontium-90.

UNIT 5: EXPONENTIAL GROWTH AND DECAY CONTINUOUS Exponential Growth and Decay Percent of change is continuously occurring during the period of time (yearly,

Aim: How do we apply the exponential function? Do Now: John bought an antique for $1000. The value of the antique has a 10% fixed increasing rate annually.

Rates of Growth & Decay. Example (1) - a The size of a colony of bacteria was 100 million at 12 am and 200 million at 3am. Assuming that the relative.

7.1 – 7.2 Practice.

EXPONENTIAL GROWTH & DECAY; Application In 2000, the population of Africa was 807 million and by 2011 it had grown to 1052 million. Use the exponential.

RADIOCARBON DATING Students will: understand the half-life of an isotope.

Differential Equations Objective: To solve a separable differential equation.

Half-Life and Doubling Time. Half-Life Phenomenon is modeled by a decreasing exponential function (shows decay). Half-life is the amount of time (length.

Section 8.2 Separation of Variables.  Calculus,10/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights.

MTH 112 Section 3.5 Exponential Growth & Decay Modeling Data.

Other Models. What we have learned Exponential Growth Model  n(t)=n 0 a t, a>1 Exponential Decay Model  n(t)=n 0 a t, 0

Exponential Growth and Decay. Objectives Solve applications problems involving exponential growth and decay.

CONTINUOUS Exponential Growth and Decay

4.1 INTRODUCTION TO THE FAMILY OF EXPONENTIAL FUNCTIONS 1.

The half-life of a radioactive isotope explains the amount of time that it takes half of the isotope in a sample to decay.

Half-life.  Half-Life - the time required for one half of a sample of a radioisotope to decay, while the other half remains unchanged  Half-lives vary.

Objective: Use exponential and logarithmic models to solve real life problems. 3.5 Exponential & Logarithmic Models 2014.

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; Newton’s Law; Logistic Models

Background Knowledge Write the equation of the line with a slope of ½ that goes through the point (8, 17)

Lesson 3.5, page 422 Exponential Growth & Decay Objective: To apply models of exponential growth and decay.

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

Modeling using Logarithms

A quantity that decreases exponentially is said to have exponential decay. The constant k has units of “inverse time”; if t is measured in days, then k.

Slide Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Chapter 5 Applications of the Exponential and Natural Logarithm Functions.

6.4 Applications of Differential Equations. I. Exponential Growth and Decay A.) Law of Exponential Change - Any situation where a quantity (y) whose rate.

3.3 Copyright © 2014 Pearson Education, Inc. Applications: Uninhibited and Limited Growth Models OBJECTIVE Find functions that satisfy dP/dt = kP. Convert.

Unit 5: Exponential Word Problems – Part 2

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

Section 3.4 – Exponential and Logarithmic Equations Section 3.5 – Exponential and Logarithmic Models.

Exponential and Logarithmic Functions

Exponential and Logarithmic Equations

3.2 Exponential and Logistic Modeling

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

Exponential and Logarithmic Models

Exponential Growth and Decay; Logistic Models

5.6 Applications and Models: Growth and Decay; and Compound Interest

Aim: How do we apply the exponential function?

Interpret Graphs 1 2 A half-life (t ) is the time required for one-half of the nuclei in a radioisotope sample to decay to products. Copyright © Pearson.

Exponential Growth and Decay

Exponential Growth and Decay; Newton’s Law; Logistic Models

Presentation transcript:

4.9 Exponential and Log/Ln Word Problems Example: Given that population is growing exponentially with the function (this is based on historical data from 1992 to 2000): Assume Population (P) is in billions t is in years since 1990 When will the population reach 10 billion?

Carbon Dating The Radio-isotope Carbon 14 decays at a constant rate and thus can be used to determine the age of any Organic material, using the ratio of carbon 14 to carbon 12. This ratio is given by: The ratio of carbon 12 to carbon 14 in a newly discovered fossil is estimate the age of the fossil.

Spread of a Virus On a college campus of 5000 students, one student returns from a vacation with a contagious and long lasting flu virus. The spread of the virus is modeled by: a) After 5 days how many students are infected? b) Classes are canceled when the number infected is 40% or more. How many days will it take for this number to be reached?

Half Life and Doubling Time Half Life – time it takes for half the material to be gone due to decay/elimination of some kind. Doubling Time – time it takes for the material of any kind to double.

Half Life/Doubling Time Example: 200 grams of radium are stored in a container. The amount R(in grams) of Radium present after t years can be modeled by: What is the half life of Radium?