# Project #32508 - Pre-Calc

Exam 3 Project - Chapters 4 and 8:
Exploring Exponential and Systems of Equations

As a review, it is recommended that you complete & submit this assignment before taking the exam.

Due Date: The original post is due by 11:59pm three (3) days before Exam 3 is due. Replies are due by 11:59pm of the last day that Exam 3 is due.

Introduction

Project:

This project will enable you to research a subject that you are interested in that has exponential growth and explore what it means for a value to grow exponentially. It will also provide insight into a system of equations and how two graphs relate to each other.

This project requires that you use TED TALKS , a site with a wide variety of informational videos for your use free of charge. The videos at the site may be used any time to further your understanding of various topics. These talks do not show you specific steps for working a problem (as did the videos at the PatrickJMT site), but they discuss general topics, including those relating to mathematics.

Activity/Process and Grading (total = 50 (40 + 5 + 5) points)

Complete all of the following activities using TED TALKS. You will submit your work to Exam 3 Project forum in Blackboard. Only submit your work in one of the following ways:

• Take a picture of your written project. Make sure it is readable. Upload the image to the discussion forum.

• Use Word and an equation editor to type your project. Make sure you answer all questions in complete sentences. Upload the file to the discussion forum.

• To snip/crop & copy an image, pull up your image/photo on the screen:

• Mac: Use Command + Shift + 4, click and drag cursor across the part of the image that you want to use. It will take a screenshot of your selected area and automatically save it to your desktop.

• Windows: Go to Start Menu>>All Programs>>Accessories>>Snipping Tool. Drag the cursor around the area that you want to capture. Name and save to your desktop.

This assignment is REQUIRED and will only be graded if resources and conclusion are part of the project. The point values for each section are noted below with an additional 10 points for replies to classmates. You are required to review at least two classmates’ projects and post a substantive reply to each (5 points for each reply for up to a total of 10 points). “Good Job” or “I didn’t think of that” will not do. You must post a follow-up question, an observation, make a suggestion, or apply some additional insight to what your classmate has posted. It is NOT your place to point out or correct errors. If you find an error that needs correcting, email your instructor for verification and the instructor will contact the student if your observation is correct.

To get started:

• Review the Example below at the bottom of this document.

• Begin by going to TED TALKS

• Search for “smart failure". The search will take you to a video is by Eddie Obeng and is calledSmart failure for a fast-changing world.

• Take notes while viewing the video.

Describing An Exponential Functions and A System of Equations: 10 points

Write several sentences describing what the talk was about and what you learned in your own words. Don’t forget to mention the exponential and linear growth described. State a description of what the input and output are as discussed in the video. On the graph, as the x-values move to the right along the x-axis, notice what is happening to the y-values. Describe what each graph represents. Then state a description of what the input and output are of each graph as discussed in the video. On the graph, as the x-values move to the right along the x-axis, notice what is happening to the y-values. Describe this change in both graphs. In the last paragraph, discuss the point where these two graphs meet and state what that point represents in the real world.

Discovering a real life example: 10 points

Recall the definition of an exponential function. Review the real life example at the end of the project and answer the questions that will help you describe it with as much detail as possible.

You will graph the function, determine the domain, find function values for random x-values and put the points in functional notation. You will also determine where the function is increasing and decreasing.

Expanding on your own real life example: 10 points

Write a real life description for exponential growth or decay. Make sure you share a picture of what you found in a graph format. Just as you did when you discovered a real life example for a quadratic function in the previous project, provide an accurate and complete description of this exponential function. Will your real life example represent how money grows in a bank account when subject to interest dividends, how the population of a city or the world grows, the growth of cancer cells, or the growth of the number of cellphone subscribers over some period of time? Or will it be the decay of a radioactive substance? Note: this last example is actually exponential decay not growth but either is acceptable. You decide. Be creative!

Showing cost and revenue: 10 points

Profit is defined as Cost minus Revenue, or P = C - R. Find an example showing cost and revenue in a textbook or on the internet. Share a picture of the graphs for cost and revenue on one coordinate system. Then discuss the input and output of each graph and describe what happens to the output as the input moves to the right along the x-axis in each graph. State the point at which the two graphs meet and describe what this means in your real life example.

Write a summary (minimum of 3 sentences) of what you learned doing this project.

Remember to list any resources you used for this project including books and or internet sites.

EXAMPLE

Recent data from past years indicate that future amounts of carbon dioxide in the atmosphere may grow according to the table below. (Amounts are given in parts per million, or ppm.) For healthy adults, CO2 becomes toxic when it reaches a level higher than 35 ppm with continuous exposure over an eight hour period. Some of the symptoms of carbon dioxide poisoning are high blood pressure, chest pains, headaches, seizures, and memory problems. Can you imagine if we all had these symptoms?

 Year Carbon Dioxide (ppm) 1990 353 2000 375 2075 590 2175 1090 2275 2000

1. Use your graphing utility to make a scatterplot of the data. Put this data into two lists, L1 and L2, using the button STAT|Edit. Then select 2nd |Y=| <enter> on 1: | <enter> on On |and then use the down arrow key and hit <enter> on the scatterplot icon | ZOOM and hit 9 for ZoomStat to graph. Remember that the years in L1 are represented on the x-axis and that CO2 levels in L2 are represented on the y-axis. Do the carbon dioxide levels appear to grow exponentially? What is the domain according to the table? Sketch the graph for submission.

2. If the function is growing exponentially, what can we state about its behavior? Is it increasing or decreasing and during which years is this happening?

3. Where does the graph hit the x-axis? Where does the graph hit the y-axis? Make a general conclusion about all exponential functions when the x-value is zero.

4. One model for the given data in the table above is the function

C(x) = 0.001942e0.00609x where the x is the year.

Using your graphing calculator, graph this function along with your scatterplot of the data. (Press the Y= button and enter the function as Y1.) Sketch this graph. According to the model, what year will the levels of carbon dioxide be 375, about 600, and about 1000? Does this line up with the data we have? To graph only the y equation inputted, go to 2nd |Y=| and select Plot1 off.

1. Use the function C(x) to predict what the levels of carbon dioxide will be in 2020. Show your algebraic work. Write your prediction as an ordered pair. Then write the values using function notation.

2. Use the function C(x) to predict when the levels of carbon dioxide will be 800 ppm. Show your algebraic work. Write this as an ordered pair. Then write the values using function notation.

3. Use the function C(x) to solve for the year when the amount of carbon dioxide is expected to double. When does it triple? Show your algebraic work.

 Subject Mathematics Due By (Pacific Time) 06/09/2014 12:00 am
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