Lesson Exponential Models

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Radiation (mr/yr) STATWAY STUDENT HANDOUT STUDENT NAME DATE INTRODUCTION TO PART 1 Radiation Levels In lesson 4.1.1 we examined the radioactivity levels in Area 2 test site in Nevada after 1985.

1 Radiation (mr/yr) STATWAY STUDENT HANDOUT STUDENT NAME DATE INTRODUCTION TO PART 1 Radiation Levels In lesson we examined the radioactivity levels in Area 2 test site in Nevada after After looking at a linear model, we found that this model was not a good fit for the data. We determined that an exponential model would be better. Let s take a look at the data and scatterplot. Year x (Years since 1985) Area 2 mr/yr , , , , , , , , , , Years

2 Radiation (mr/yr) STATWAY STUDENT HANDOUT 2 Notice that while the graph of the data appears to be linear, we can get a better fit with an exponential curve Years TRY THESE 1 Looking at the graph would you say the radiation levels are increasing or decreasing over time? Explain your reasoning. 2 This data was collected 3 years after the last nuclear testing. Use the model to estimate what the levels were immediately following the last explosion in 1985.

3 Users (millions) STATWAY STUDENT HANDOUT 3 Facebook membership In February 4, Facebook was born as a social networking tool. The company has been tracking its membership since December 4. Below you will find membership counts (in millions) for some months between December 4 and July month-yr x (Months since Feb-04) Facebook users (millions) Dec Dec Dec Apr Oct Aug Jan Feb Apr Jul Sep Months Dec Feb Jul

4 STATWAY STUDENT HANDOUT 4 TRY THESE 3 Looking at the graph would you say that the data fits a linear pattern? 4 Explain your answer. 5 If not linear, which non-linear model would best fit the data? 6 Looking at the graph would you say the membership increasing or decreasing over time? Explain your answers in problems 5 and 6.

5 Users (millions) STATWAY STUDENT HANDOUT 5 Let s fit the model to the data Months NEXT STEPS 7 Use the model to estimate what the membership was in July 6 (month 28), June 7 (month 40) and March 8 (month 49)? Use the equation to find these. 8 Would these estimates be reliable? Explain. 9 Use the model to estimate what the membership was in Mar 2011 (month 85)? 10 Is the estimate you found in (9) reliable?

6 STATWAY STUDENT HANDOUT 6 11 Membership data was not reported until 8 months after Facebook began. Use the graph to estimate the number of users when Facebook started in February 4 (month 0)? Is this starting value in the exponential model? TRY THESE 12 Referring back to the equation for the radiation level of Area 2,, what value in the equation indicates that this is an example of exponential decay? 13 How do you know this is exponential decay and not exponential growth? 14 Identify which of the following equations is an example of exponential decay and list them in order from the fastest rate of decay to the slowest. Equation A: Equation B: Equation C: 15 Referring back to the equation for Facebook membership, what value in the equation indicates that this is an example of exponential growth?

7 STATWAY STUDENT HANDOUT 7 16 How do you know this is exponential decay and not exponential growth? 17 Identify which of the following equations is an example of exponential growth and list them in order from the fastest rate of growth to the slowest. Equation A: Equation B: Equation C:

8 Radiation (mr/yr) Radiation (mr/yr) STATWAY STUDENT HANDOUT 8 TAKE IT HOME 1 In the homework for lesson you examined the Radioactivity levels in Area 4 test site in Nevada after After looking at a linear model, you found that this model was not a good fit for the data. Below you will find the data represented in a scatterplot and fitted with the exponential model. Answer the following questions Years Years A Does this look like exponential growth, decay, or neither? Explain your answer. B Use the graph to estimate the radiation levels of Area 4 in June 1992 and June (Hint: if June 1987 is 2.5 years after 1985, the time would be 2.5 years.) C Use the exponential equation to find the estimates for the radiation level of Area 4 in June 1992 and June Are these estimates considered reliable? Explain.

9 STATWAY STUDENT HANDOUT 9 D Use the graph to estimate the radiation level of Area 4, immediately following the last explosion in E Use the exponential equation to estimate the radiation level of Area 4, immediately following the last explosion in F Is the estimate found in (E) reliable? Explain. 2 The population (in millions) for Madagascar in years since 0 can be approximated by the equation. A State the approximate population of Madagascar in 0. Explain. B Is the population decaying or growing? Explain. 3 The quantity of Ibuprofen (in mg) remaining in your blood stream after hours can be approximated by the equation. A State the approximate dose of Ibuprofen that was taken. Explain. B Is the dose in the bloodstream decaying or growing? Explain.

10 STATWAY STUDENT HANDOUT This lesson is part of STATWAY, A Pathway Through College Statistics, which is a product of a Carnegie Networked Improvement Community that seeks to advance student success. Version 1.0, A Pathway Through Statistics, Statway was created by the Charles A. Dana Center at the University of Texas at Austin under sponsorship of the Carnegie Foundation for the Advancement of Teaching. This version 1.5 and all subsequent versions, result from the continuous improvement efforts of the Carnegie Networked Improvement Community. The network brings together community college faculty and staff, designers, researchers and developers. It is an open-resource research and development community that seeks to harvest the wisdom of its diverse participants in systematic and disciplined inquiries to improve developmental mathematics instruction. For more information on the Statway Networked Improvement Community, please visit carnegiefoundation.org. For the most recent version of instructional materials, visit Statway.org/kernel STATWAY and the Carnegie Foundation logo are trademarks of the Carnegie Foundation for the Advancement of Teaching. A Pathway Through College Statistics may be used as provided in the CC BY license, but neither the Statway trademark nor the Carnegie Foundation logo may be used without the prior written consent of the Carnegie Foundation.

Math 181, Calculus I

Math 181, Calculus I [Semester] [Class meeting days/times] [Location] INSTRUCTOR INFORMATION: Name: Office location: Office hours: Mailbox: Phone: Email: Required Material and Access: Textbook: Stewart,