Exponential Functions. When do we use them? Exponential functions are best used for population, interest, growth/decay and other changes that involve.

Slides:

Advertisements

Similar presentations

Unit 9. Unit 9: Exponential and Logarithmic Functions and Applications.

Advertisements

Write an exponential function

 In the 2 scenarios below, find the change in x and the change in y.  What conclusions can you draw? What are the similarities & differences? How would.

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

Chapter 10 Regression. Defining Regression Simple linear regression features one independent variable and one dependent variable, as in correlation the.

Chapter Four: More on Two- Variable Data 4.1: Transforming to Achieve Linearity 4.2: Relationships between Categorical Variables 4.3: Establishing Causation.

FACTOR THE FOLLOWING: Opener. 2-5 Scatter Plots and Lines of Regression 1. Bivariate Data – data with two variables 2. Scatter Plot – graph of bivariate.

EXAMPLE 5 Find a power model Find a power model for the original data. The table at the right shows the typical wingspans x (in feet) and the typical weights.

SOFTBALL EXAMPLE 3 Predict using an equation The table shows the number of participants in U.S. youth softball during the period 1997–2001. Predict the.

Transformations to Achieve Linearity

MAC 1105 Section 4.3 Logarithmic Functions. The Inverse of a Exponential Function 

Copyright © Cengage Learning. All rights reserved.

Quadratic t n = an 2 + bn + c Ex: Find the generating function for the following: A) 2, 7, 16, 29, 46, 67, /5 students can do a Quad Reg on the.

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, ∞)

Exploring Exponential Functions

1 6.9 Exponential, Logarithmic & Logistic Models In this section, we will study the following topics: Classifying scatter plots Using the graphing calculator.

Splash Screen. Concept Example 1A Use a Scatter Plot and Prediction Equation A. EDUCATION The table below shows the approximate percent of students who.

1.5 Cont. Warm-up (IN) Learning Objective: to create a scatter plot and use the calculator to find the line of best fit and make predictions. (same as.

Sec 4.1 Exponential Functions Objectives: To define exponential functions. To understand how to graph exponential functions.

Exponential Functions y = a(b) x Exponential Growth This graph shows exponential growth since the graph is increasing as it goes from left to right.

Advanced Precalculus Notes 4.9 Building Exponential, Logarithmic, and Logistic Models.

Exponential Regression Section Starter The city of Concord was a small town of 10,000 people in Returning war veterans and the G.I.

5.5 Objectives Apply the base properties of logarithms. Use the change of base formula.

Section 2.6 – Draw Scatter Plots and Best Fitting Lines A scatterplot is a graph of a set of data pairs (x, y). If y tends to increase as x increases,

* SCATTER PLOT – GRAPH WITH MANY ORDERS PAIRS * LINE OF BEST FIT – LINE DRAWN THROUGH DATA THAT BEST REPRESENTS IT.

Scatter Plots, Correlation and Linear Regression.

© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 7 Algebra: Graphs, Functions, and Linear Systems.

2.5 Using Linear Models A scatter plot is a graph that relates two sets of data by plotting the data as ordered pairs. You can use a scatter plot to determine.

Objective: To write linear equations that model real-world data. To make predictions from linear models. Bell Ringer: Write 3 ways you used math over your.

Section 3.5 Modeling with Exponential Logarithmic Functions.

Aim: Graph of Best Fit Course: Alg. 2 & Trig. Aim: How do we model real-world data with polynomial and other functions? Do Now: 6 pt. Regents Question.

Holt McDougal Algebra Curve Fitting with Exponential and Logarithmic Models 4-8 Curve Fitting with Exponential and Logarithmic Models Holt Algebra.

How do we model data by using exponential and logarithmic functions?

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

Constructing Nonlinear Models Lesson 5.7. Modeling Data When data are recorded from observing an experiment or phenomenon May increase/decrease at a constant.

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

Regression and Median Fit Lines

Scatter Plots. Scatter plots are used when data from an experiment or test have a wide range of values. You do not connect the points in a scatter plot,

Chapter Nonlinear models. Objectives O Classify scatterplots O Use scatterplots and a graphing utility to find models for data and choose the model.

Regression Line  R 2 represents the fraction of variation in the data (regression line)

Statistics: Scatter Plots and Lines of Fit. Vocabulary Scatter plot – Two sets of data plotted as ordered pairs in a coordinate plane Positive correlation.

1.6 Modeling Real-World Data with Linear Functions Objectives Draw and analyze scatter plots. Write a predication equation and draw best-fit lines. Use.

LOGARITHMIC AND EXPONENTIAL EQUATIONS LOGARITHMIC AND EXPONENTIAL EQUATIONS SECTION 4.6.

Over Lesson 3-4 5–Minute Check 1 Solve 9 x – 2 = 27 3x. A. B.–1 C. D.

The relationship between cost and home sales

Applications and Models: Growth and Decay; and Compound Interest

CHAPTER 5: Exponential and Logarithmic Functions

Solving Exponential and Logarithmic Equations

1.3 Exponential Functions Day 1

Exponential and Logistic Modeling

Applications and Models: Growth and Decay; and Compound Interest

Exponential and Logarithmic Data Modeling

Strong Positive Strong Positive Weak Positive Strong Negative

Mathematics of Population Growth

Express the equation {image} in exponential form

Deriving and Integrating Logarithms and Exponential Equations

Ch. 12 More about regression

Constructing Nonlinear Models

Section 5.6 Natural Logarithms.

Scatter Plots and Best-Fit Lines

Exponential and Logarithmic Forms

y = mx + b Linear Regression line of best fit REMEMBER:

Ch 4.1 & 4.2 Two dimensions concept

Which graph best describes your excitement for …..

Can you use scatter plots and prediction equations?

Presentation transcript:

Exponential Functions

When do we use them? Exponential functions are best used for population, interest, growth/decay and other changes that involve a rapid increase or decrease in data values. Exponential functions: y = a(b x ) Logarithmic functions: y = a + b ln x Logistic growth functions:

Let’s experiment! Enter the data in the table into your calculators for L 1 and L 2 Plot the data on your calculator X, years since 1969 Y, federal minimum wage

Exponential Regression Use your calculator to find the exponential regression equation. How well does the correlation coefficient, r, indicate that the model fits the data? Use this equation to predict the minimum wage in 2009.

Logarithmic regression Use your calculator to find the logarithmic regression equation. How well does the correlation coefficient, r, indicate that the model fits the data? Use this equation to predict the minimum wage in 2009.

Power Regression Use your calculator to find the power regression equation. How well does the correlation coefficient, r, indicate that the model fits the data? Use this equation to predict the minimum wage in 2009.

Which is best? Based on the correlation coefficients, which model will give the best prediction for minimum wage in the future? Based on this model that you chose, by which year will the minimum wage be $7.25?

How did we do? The federal minimum wage in 2009 was $7.25. How well did our equation do at predicting the future? Is this a fair model to continue using for future predictions?