2: Provide a brief description of each of the four components of a linear function. For...

  
 

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2: Provide a brief description of each of the four components of a linear function. For each of the three scenarios below, provide the following, and answer the question included with each scenario. A: What is the initial value? What context clues indicate this to you? B: What is the rate of change? What context clues indicate this to you? C: What value of the independent or dependent variable are you tasked to work with? Scenario 1: A group of climbers begin climbing at an elevation of 6500 feet and ascend at a steady rate of 600 vertical feet per hour. What is their elevation after 3.5 hours? Write the equation you used to determine your answer. For actual climbing, does a steady rate of 600 vertical feet per hour make sense in all climbing environments? Support your response. Scenario 2: The diameter of a tree increases by 0.2 inch with each passing year. When you started observing the tree, its diameter was 4 inches. Estimate the time at which the tree began growing. I Scenario 3: The cost of publishing a poster is $2000 for setting up the printing equipment, plus $3 per poster printed. What is the total cost to produce 2000 posters? Write an equation that can be used to find the cost to produce any number of posters. A competing printer takes $1800 for setup and costs $6 per poster printed. What is the total cost to produce 2000 posters? See if you can estimate the number of posters for which either setup is the same cost. Follow up: 1: In general, how many pieces of information do you need in order to create a linear function? 2: Linear change is not the same as exponential change. Provide a brief contrast of the two and indicate a piece of information that, if given, would indicate to you something can be modeled by a linear function. You can reference the 3 scenarios above to assist in finding your response. I 2: Provide a brief description of each of the four components of a linear function. For each of the three scenarios below, provide the following, and answer the question included with each scenario. A: What is the initial value? What context clues indicate this to you? B: What is the rate of change? What context clues indicate this to you? C: What value of the independent or dependent variable are you tasked to work with? Scenario 1: A group of climbers begin climbing at an elevation of 6500 feet and ascend at a steady rate of 600 vertical feet per hour. What is their elevation after 3.5 hours? Write the equation you used to determine your answer. For actual climbing, does a steady rate of 600 vertical feet per hour make sense in all climbing environments? Support your response. Scenario 2: The diameter of a tree increases by 0.2 inch with each passing year. When you started observing the tree, its diameter was 4 inches. Estimate the time at which the tree began growing. I Scenario 3: The cost of publishing a poster is $2000 for setting up the printing equipment, plus $3 per poster printed. What is the total cost to produce 2000 posters? Write an equation that can be used to find the cost to produce any number of posters. A competing printer takes $1800 for setup and costs $6 per poster printed. What is the total cost to produce 2000 posters? See if you can estimate the number of posters for which either setup is the same cost. Follow up: 1: In general, how many pieces of information do you need in order to create a linear function? 2: Linear change is not the same as exponential change. Provide a brief contrast of the two and indicate a piece of information that, if given, would indicate to you something can be modeled by a linear function. You can reference the 3 scenarios above to assist in finding your response. I