A popular fall activity is picking apples, but did you know that the growth of an...

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A popular fall activity is picking apples, but did you know that the growth of an apple tree can actually be modelled by using a logarithmic curve. STEP 1: (Table created with random numbers from the Google sheet) Year 1 2 3 4 5 6 7 8 9 Height of Tree ft) 7 17 21 24 27 29 31 33 33 STEP 2: (Graphing with Desmos) Link to Desmos Graph Let the x-axis be equal to years. Let the y-axis be equal to height. 1 2 3 4 5 6 7 8 9 7 17 21 24 27 29 31 33 33 -10 desmos -30 20 10 0 · . 10 20 STEP 3: Determine a logarithmic function (in the form y = a + b logx) for the curve of best fit for your data. Show all of your work and explain how you determined the best model to fit the data. STEP 4: Using your table and/or scatter plot, make the following predictions and then justify your predictions algebraically using the function you developed: a) How tall will the tree be at 30 months? b) How tall will the tree be in 15 years? c) When will the tree reach a height of 10 feet? d) When will the tree reach a height of 25 feet? STEP 5: Using your scatter plot from Step 2, graph the logarithmic function you determined in Step 3 on the same graph. Reflect upon the accuracy of your function. Are there any other transformations you could have applied to your logarithmic function to improve its fit? Step 6: Explain why a logarithmic model works in this situation. For what other situations might this model be appropriate? A popular fall activity is picking apples, but did you know that the growth of an apple tree can actually be modelled by using a logarithmic curve. STEP 1: (Table created with random numbers from the Google sheet) Year 1 2 3 4 5 6 7 8 9 Height of Tree ft) 7 17 21 24 27 29 31 33 33 STEP 2: (Graphing with Desmos) Link to Desmos Graph Let the x-axis be equal to years. Let the y-axis be equal to height. 1 2 3 4 5 6 7 8 9 7 17 21 24 27 29 31 33 33 -10 desmos -30 20 10 0 · . 10 20 STEP 3: Determine a logarithmic function (in the form y = a + b logx) for the curve of best fit for your data. Show all of your work and explain how you determined the best model to fit the data. STEP 4: Using your table and/or scatter plot, make the following predictions and then justify your predictions algebraically using the function you developed: a) How tall will the tree be at 30 months? b) How tall will the tree be in 15 years? c) When will the tree reach a height of 10 feet? d) When will the tree reach a height of 25 feet? STEP 5: Using your scatter plot from Step 2, graph the logarithmic function you determined in Step 3 on the same graph. Reflect upon the accuracy of your function. Are there any other transformations you could have applied to your logarithmic function to improve its fit? Step 6: Explain why a logarithmic model works in this situation. For what other situations might this model be appropriate?

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Given table Year Height of Tree ft 1 7 2 17 3 21 4 24 5 27 6 29 7 31 8 33 9 33 To determine the loga... View the full answer