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.

Slides:

Advertisements

Similar presentations

Whether does the number e come from!?!?. Suppose the number of bacteria, n 0, in a dish doubles in unit time. If a very simple growth model is adopted,

Advertisements

Section 6.7 – Financial Models

Section 3.2b. In the last section, we did plenty of analysis of logistic functions that were given to us… Now, we begin work on finding our very own logistic.

Quiz 3-1 This data can be modeled using an Find ‘a’

Copyright © 2011 Pearson, Inc. 3.2 Exponential and Logistic Modeling.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 3.1 Exponential and Logistic Functions.

Chapter 3 Exponential, Logistic, and Logarithmic Functions

Exponential and Logistic Modeling

CHAPTER Continuity Exponential Growth and Decay Law of Natural Growth(k>0) & (Law of natural decay (k

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,

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

Chapter 3 Linear and Exponential Changes 3.2 Exponential growth and decay: Constant percentage rates 1 Learning Objectives: Understand exponential functions.

Differential Equations

Exponential Growth and Decay

1.3 Exponential Functions Acadia National Park, Maine.

Exponential Growth & Decay By: Kasey Gadow, Sarah Dhein & Emily Seitz.

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

Algebra 2.  The _______________ number …. is referred to as the _______________________.  An ___________ function with base ___ is called a __________.

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

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

Sullivan PreCalculus Section 4

Exponential Growth and Decay; Modeling Data

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

Homework Lesson Handout #5-27 (ODD) Exam ( ): 12/4.

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,

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

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

7-5 Exponential and Logarithmic Equations and Inequalities Warm Up

Exponential Functions Chapter 1.3. The Exponential Function 2.

Applications of Exponential Functions. Radioactive Decay Radioactive Decay The amount A of radioactive material present at time t is given by Where A.

Applications and Models: Growth and Decay

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.

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 and Logistic Functions. Quick Review.

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.

11/23/2015 Precalculus - Lesson 21 - Exponential Models 1 Lesson 21 – Applications of Exponential Functions Precalculus.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3- 1 Homework, Page 286 Is the function an exponential function? If.

Exponential Modeling Section 3.2a.

MTH 112 Section 3.5 Exponential Growth & Decay Modeling Data.

Pg. 282/292 Homework Study #7$ #15$ #17$ #1x = 2 #2x = 1#3x = 3 #4x = 4 #5x = -4 #6x = 0 #7no solution #8x = 2 #9Graph #10Graph #11Graph.

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.

Advanced Precalculus Notes 4.8 Exponential Growth and Decay k > 0 growthk < 0 decay.

Section 3.5 Modeling with Exponential Logarithmic Functions.

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.

Warm Up: Find the final amount : Invest $4000 at 6% compounded quarterly for 20 years. Invest $5600 at 3.7% compounded continuously for 12 years.

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

6.7 Growth and Decay. Uninhibited Growth of Cells.

Various Forms of Exponential Functions

Chapter 5 Applications of Exponential and Natural Logarithm Functions.

1 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 3.1 Exponential Functions Demana, Waits, Foley, Kennedy.

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.

Exponential and Logarithmic Functions 4 Copyright © Cengage Learning. All rights reserved.

Entry Task Solve. 1. log16x = 2. log10,000 = x

CHAPTER 5: Exponential and Logarithmic Functions

3.2 Exponential and Logistic Modeling

1.3 Exponential Functions Day 1

Exponential and Logistic Modeling

Applications and Models: Growth and Decay; and Compound Interest

Exponential and Logistic Modeling

Exponential Functions

5.4 Applications of Exponential Functions

1.3 Exponential Functions

Exponential Growth and Decay

Warm up honors algebra 2 3/7/19

Presentation transcript:

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 a population P is changing at a constant percentage rate r each year, then P(t) = P 0 (1 + r) t Where P 0 is the initial population, r is expressed as a decimal, and t is time in years. If a population P is changing at a constant percentage rate r each year, then P(t) = P 0 (1 + r) t Where P 0 is the initial population, r is expressed as a decimal, and t is time in years. (1 + r) 1.42% decay Determine the exponential function with initial value = 12, increasing at a rate of 8 % per year?

Modeling bacteria growth Suppose a culture of 100 bacteria is put in a petri dish and the culture doubles every hour. Predict when the number of bacteria will be 350,000. doubles means what %? what is the initial population? represents the bacteria population t hours after placed in the petri dish. Use the graphing calculator to calculate the intersection when y = 350,000 Intersection: ( , ) 11 hr + ( )60 min The number of bacteria will be 350,000 in 11 hours and 46 minutes.

Modeling radioactive decay Suppose the half-life of a certain radioactive substance is 20 days and there are 5 g present initially. Find the time when there will be 1 g of the substance remaining. half-life means what %? not daily, every 20 days means? Use the graphing calculator to calculate the intersection when y = 1 Intersection: ( , 1) 46 days + ( )24 hrs There will be 1 g of the radioactive substance remaining after approximately 46 days and 11 hours. t per 20 days Initial population? Models the mass in grams of the radioactive substance at time t days.

DAY 2 Modeling using exponential regression Use the data table and exponential regression to predict the U.S. population for Compare the result with the listed value for Use STAT to enter data in L 1 and L 2 Do not enter data for year 2000 Graph using STAT PLOT.

Modeling using exponential regression Use the data table and exponential regression to predict the U.S. population for Compare the result with the listed value for Use STAT then CALC to write an exponential regression model for the data The exponential regression predicts the population will be million. Use the TRACE to calculate the population for the year Compare the result with the listed value for – = 12.9 It is overestimated by 12.9 million, less than a 5 % error.

Modeling using logistic regression Use the data table and logistic regression to predict the maximum sustainable populations for Florida and Pennsylvania. Use STAT to enter data in L 1, L 2 and L 3 Graph using STAT PLOT. Use different symbols for each graph. [0,210] by [-5,20]

Modeling using logistic regression Use the data table and logistic regression to predict the maximum sustainable populations for Florida and Pennsylvania. Use STAT then CALC to write a logistic model for the data Predict the maximum sustainable populations: The maximum sustainable population for Florida is about 28.0 million and for Pennsylvania is about 12.6 million.

Exponential and Logistic Modeling