Algebraic and Transcendental Functions Exponential Growth and Decay: Multicultural Project By: Arq. Ma. Teresa Cantú Elizondo

Transcription

1 Algebraic and Transcendental Functions Exponential Growth and Decay: Multicultural Project By: Arq. Ma. Teresa Cantú Elizondo Ana Karen Hinojosa Roberto Salinas Sebastián Elizondo Andrés Hernández Eugenio Guevara a a a a a

2 Algebraic and Transcendental Functions Exponential Growth and Decay: Multicultural Project By: Arq. Ma. Teresa Cantú Elizondo Objectives: General: Understand the concept of exponential growth and decay. Analyze the behavior, translations and main characteristics of the graphs of exponential functions. Specific: 1. Explain the concept of exponential growth and decay and the graph that represents its function. 2. Use technological and digital resources to present the concept of exponential growth and decay and the graph that represents it. 3. Reflect upon global environmental consequences and impact of the use of nuclear energy. DESCRIPTION Teacher asks students to comment and discuss in class what it is that they know about the Chernobyl 1986 disaster. Teacher explains the concept of exponential growth and decay, the equation that represents it and the main characteristics of its basic graph. Students in teams of 4 (from a different campus) make a summary that contains facts, consequences and implications of the Chernobyl Nuclear Reactor Disaster to this day and in a global context. Students Students in teams of 4 (from a different campus) are asked to do more research and find two real situations or events that also represent exponential growth and decay. Students in teams of 4 (from a different campus) share their individual conclusions using any form of social media they want and generate a team conclusion that includes a solution proposal that has a reflection on this incident and its environmental consequences in a global scale. The product is one YouTube video per team.

3 ACTIVITY Kickoff: Teacher in the classroom or as flipped class asks the following questions; Why hasn t it been possible to contain the nuclear energy and substances generated by the nuclear reactor s explosion in Chernobyl in 1986? Because the nuclear energy had a high amount of radiation and due to this the substances were not balanced and overpassed the main points where they should have been. What is that makes nuclear energy to be so dangerous? Because even with a small amount of extra radiation an explosion can be ocurre. Nuclear energy is very delicate so people have to take into account which are the right measurements for preventing accidents. Why is it said that a nuclear reaction generates an exponential growth of the atoms? A reaction happens when the substances that have a low tolerance rate or are highly reactive stand near each other causing the atoms to move faster and creating the reaction. Since the atoms are moving faster this means that also the generation of them is also fast. When will all the nuclear energy and substances released by this explosion be dissolved, can they be cleaned out completely? The energy from the explosion will remain there for the next 20,000 years, but there is not an specific idea of how much years will it take for Chernobyl being habitable again, because when the reactor exploded in Chernobyl the soil became radioactive, also because the release of the radiation was in big amount and for long periods of time and because when the reactor exploded 7 tons of nuclear fuel was exposed into the environment. Teacher explains the concept of exponential growth, the equation that represents it and the main characteristics of its basic graph using the following video

4 Part I: Students in teams of 4 (from a different campus), make a visual / graphic summary where they clearly show and explain the basic graph that represents an exponential function that includes its reference point, its domain and its range.

5 Part II: To be done by students in teams of 4 (from a different campus): Watch the following videos that contain documentaries with more information on the topic. They are to be watched and discussed by all team members. As a team, you must make a summary that contains facts, consecuences and implications of the Chernobyl Nuclear Reactor Disaster to this day and in a global context. and As a team you are to do research and present with facts, at least two different real situations or events that are examples of exponential growth and decay. Clearly justify your examples. Your team work and sharing of information can be done any way you want. You can meet and work together, use google docs, google hangouts, facebook, facetime, skype, whatsapp, etc. Note: Your final product must include at least 2 evidences that clearly shows how you interacted and worked as a team. Conclusions: Students in teams of 4 (from a different campus) write a team s conclusion that must give an answer to each of the following questions: What is exponential growth? What is the function and graph that models and represents it? Is when something raises in an exponential way, this means is when it multiplies itself several times, a model for growth of a quantity in which the rate of growth is proportional to the amount given. What are their main characteristics? (include a picture of your team s visual / graphic summary) What is exponential decay? Formula for exponential growth: y(t)= a * e ^kt The main characteristics of an exponential growth is that the something rises in a specific rate. An exponential decay is the same, but instead of rising, the values falls. What are the implications of using nuclear energy? Do you consider nuclear energy to be clean energy? (justify your answer) Nuclear energy is very useful to humans, however this type of energy is very dangerous since it can cause lots of sickness and deaths, as we could see in Chernobyl s problem and that s why some scientists are doubting if it really is worth it to keep using this type of energy source. I do not consider nuclear energy a clean energy because a clean energy does not causes lots of problems and dangers to the society and to the environment.

6 Are you aware that there is a Nuclear Energy Plant in Mexico? Where is it? Do you think it is safe? Do you agree with the fact that there is a Nuclear Energy plant in your country? (Justify your answer) Yes I am aware that there is tho in Mexico, the Nuclear Energy Plant in Mexico are located in Mexico City and in Laguna Verde. I do not think they are safe, since they could make an effect of a massive explosion and cause impressive accidents on living things. I do not agree with the fact that there is a nuclear energy plant in Mexico because the outcomes in case of a failure are massive disasters, maybe having one where everything is protected could work. Could the Chernobyl 1986 nuclear disaster have been prevented? How? Once the explosion happened, was there any way to stop the radiation spread and its pollution? Do you think that the radioactive pollution generated by this disaster reached Mexico? (Justify your answer). What are at least 4 environmental consequences (in a global scale) of the Chernobyl 1986 disaster? Yes, there were three ways to stop it, one by not testing the turbines, the second way by sending the workers that knew about the project and the third way by simply not having nuclear plants. There was no way to stop the spreading because radiation is not that easily controlled. No, it did not reached Mexico, it barely reached some european countries, so there is no way it could have reached Mexico. Some of the consequences that this explosion caused is that there can t be humans living in there, water is not longer drinkable, deformation in animals, and the trees suffered. What are the environmental consequences (in a global scale) of other nuclear disasters and use of nuclear weapons? Nuclear disasters and attacks could end all life on Earth and this types of problems are too difficult to prevent, like Chernobyl s disaster, there are a lot of problems that repercussions that come from radiation and we have seen them in USA s attack to Japan. Some effects that can happen due to nuclear weapons are the increase of temperature on a scale that it could make the skin of living things to turn into dust, also oxygen could be gone by the pass of the time. Also most of the trees and plants would be dead because of the burns and globally the temperature would get higher. What do you think and feel about these consequences? What would be a solution proposal for this situation? I feel impressed about the consequences because the effect lasts on the Earth for a large amount of time and also because all the effects are extremely bad and difficult to be fixed. A solution for this kind of situation is to stop using nuclear plants, or if they want to use them to be highly careful and to have them on a place where the damage is not that big on living things. How did we feel working like this? Did we like it? Was it difficult? What did I like the most of working with my teammates in this form?

7 We felt that the project was easy when everybody gave their ideas and points of view but it was difficult to have communication since half of the team is on another campus. I liked working on drive because everybody can have the same information and add more. Closure: Teacher in class has a group discussion on the questions that were answered for the project s conclusions. Final Product: The link to your team s YouTube video is to be uploaded in the corresponding Blackboard Discussion board by Monday October 17, 2016 at 11:59 pm. Be sure that your team s video is uploaded as public so that your teacher is able to watch it. If your teacher is not able to access it and watch it, your grade in the project is going to be zero, no exceptions. This final product must include the following: Introduction with complete Names, Id Numbers and campus of all team members must be clearly shown. A brief summary of the project s contents. Part I with a visual / graphic summary where students clearly show and explain the basic graph that represents an exponential function that includes its reference point, its domain and its range. Part II with the summary of the Chernobyl Nuclear Disaster and at least two different real events / situations that are also examples of exponential growth and decay. Also include, evidence of the team s interaction and form or work. Conclusions with the answers to the questions provided in the activity. Due date: October XXXX, 2017 by 23:59:59 This activity will count as the 2nd Partial Project and will have the corresponding value. The complete project, and its conclusion must be included in each student s portfolio. EVIDENCE

8 REFERENCES Thyroid Cancer - Topic Overview. (n.d.). Retrieved October 15, 2017, from (n.d.). Netflix: revenue in Retrieved October 12, 2017, from Campaign for Nuclear Disarmament. (n.d.). Retrieved October 16, 2017, from Chernobyl Disaster's Agricultural and Environmental Impact. (n.d.). Retrieved October 16, 2017, from

9 RUBRIC Name: Id#: Group: Percentage Product Points deo s clarity and quality of image and sound. All team members actively participate in equal portions of the video. munication of ideas, theory, concepts, facts, summaries and anations is clear and correct. Evidence of team members action is included. and expression of mathematical notations, symbols and esentations (both oral and written expressions) is clear and ect. duction: Name, Id#, Campus and brief summary of project. I: Visual / graphic summary of the graph that represents onential functions with all of its elements. II: Summary of Chernobyl disaster and at least 2 examples of onential growth and decay with two other real events / situations. clusions: Answers to all questions and solution proposal. Total Points: