Unit Activity Essays (1019 words) - Mathematics, Elementary Algebra

Unit Activity Unit: Two-Variable Equations, Inequalities, and Graphs This activity will help you meet these educational goals: Mathematical Practices-You will make sense of problems and solve them, reason abstractly and quantitatively, use mathematics to model real-world situations, and look for and express regularity in repeated reasoning. Introduction In this unit, you used different methods to create and solve linear equations. You modeled scenarios using linear inequalities and solved them with the help of graphs. In this activity, you will analyze real-world situations by modeling them as equations and looking at their graphs. __________________________________________________________________________ Directions and Analysis Task 1: Deforestation [pic] There are approximately 400 million trees currently growing in the Amazon Rainforest, which covers approximately 5.5 million square kilometers. The rainforest is being cleared at a rate of 20,000 square kilometers per year to make way for new farmland and to harvest wood for building supplies. Before this year, 250,000 square kilometers had already been cleared. A preservation consortium is trying to mitigate the loss of rainforest by planting new trees. They have already planted 3,000 square kilometers of trees and plan to plant 100 square kilometers of trees each year. a. Create an equation to represent the rainforest area deforested, AD, in thousands of square kilometers, after t years. Type your response here: b. Create an equation to represent the rainforest area planted with new trees, AP, in thousands of square kilometers, after t years. Type your response here: c. Use the Edmentum Graphing Tool to graph the equations you created in parts a and b. Specify what each axis represents, and set the scale of each graph to ensure a good view of both graphs. Copy both graphs and paste them in the answer area below. Type your response here: d. How did you choose the scales you used for the graphs? How does using different scales affect the way you compare the two graphs? Type your response here: e. What are the y-intercepts of each function, and what do they represent? Type your response here: f. What area will have been cleared due to deforestation after 1 year, 5 years, and 10 years? Type your response here: |Years From Now |Total Area | | |Cleared | | |(1,000 sq km) | |1 | | |5 | | |10 | | g. What area will have been planted by the preservation consortium after 1 year, 5 years, and 10 years? Type your response here: |Years From Now |Total Area | | |Planted | | |(1,000 sq km) | |1 | | |5 | | |10 | | h. What percentage of the area lost to deforestation will have been replanted by the preservation consortium after 1 year, 5 years, and 10 years? Type your response here: |Years From Now |Percentage | |1 | | |5 | | |10 | | i. Based on your findings, will the preservation consortium ever be able to restore the rainforest to its original size before it is completely cleared? Explain. Type your response here: Task 2: Driving Out of Town [pic] Brent is driving to a conference in another state. Three hours after leaving his home and beginning his drive, Brent is still 470 miles from his destination. After another 4 hours of driving, Brent is 258 miles from his destination. After 9 hours of driving, Brent plans to stop at a hotel for the night and begin his trip again 12 hours later. a. Use the given information to determine the coordinates of two points that represent Brent's distance from his destination based on the amount of time he has spent driving. Type your response here: b. Assuming that Brent's average rate of speed stays consistent during his entire drive, create an equation to represent the distance left to his destination, d, based on the amount of time he has spent driving, t. Write the equation in slope-intercept form. Type your response here: c. Use the Edmentum Graphing Tool to graph the line represented by the equation. Let x represent t and y represent d. Set the scale so the graph can be easily seen and paste the graph below. Type your response here: d. What are the intercepts of the equation, and what do they represent? Type your response here: e. What does the slope of the line represent? Type your response here: f. If Brent's average speed had been faster or slower on his trip, what features of the graph would change and how would they change in each situation. Explain your answers. Type your response here: g. Brent decided that