Algebra 2 - Borges

Mathematical Modeling

Procedure

Part 1. Determine a mathematical model for the mass of puzzle pieces as a function of the number of wooden cubes in the piece. Then use the mathematical model to make predictions.

  1. Record the number of cubes and mass of each of your puzzle pieces.

Color of Piece / Number of Cubes / Mass (g)
  1. Graph your data points using Google Sheetsbelow such that the number of cubes in the puzzle piece is represented on the x-axis and the mass of the piece is indicated on the y-axis. Label the axes and indicate units.
  1. Consider the data that you have graphed and answer the following.
  2. Would you expect that this data is linear; that is, if you were to measure the mass of other pieces with more than six cubes or fewer than four cubes, would the points fall on a straight line on the graph? Explain your answer.
  1. Based on your data, what would you predict for the mass of a single wooden cube? Explain your answer.
  1. Using your predicted y-intercept, sketch a trend linefor your data on the grid above. (Insert Graph Here)
  1. What is the slope of your line-of-best-fit? Explain the interpretation of the slope in words.
  1. Write the equation for your line of best fit.
  1. Estimate the mass of a puzzle piece that includes two wooden cubes. Show your work.
  1. If a puzzle piece has a mass of 31.5 grams, how many wooden cubes would you predict were used to create the puzzle piece? Show your work.

Part 2. Find a mathematical model to represent the minimum jump height of a BMX bike as a function of the bike weight. Then use the mathematical model to make predictions.

  1. An engineer is redesigning a BMX bike. He is interested in how the weight of the bike affects the height that the bike reaches when the rider “gets air” or jumps the bike off of a ramp. He asked an experienced rider to test bikes of various weights and recorded the following minimum jump heights.

Bike Weight
(lb) / Minimum Jump Height (in.)
19 / 83.5
19.5 / 82.0
20 / 79.2
20.5 / 77.1
21 / 74.9
22 / 73.3
22.5 / 71.0
23 / 68.1
23.5 / 65.8
24 / 64.2

Use this data to complete each of the following.

  1. Create a scatterplot and find a trend line for the data using Google Sheets. Insert scatterplot here.
  1. Write the equation relating Bike Weight to Minimum Jump Height in function notation.
  1. What is the domain of the function? Explain.
  1. What is the range of the function?
  1. What is the slope of the line (include units). Is the slope positive or negative? Explain the interpretation of the slope in words.
  1. If the minimum jump height of 89.7 inches is recorded, predict the estimatedweight of the bike. Show your work.

Conclusion

  1. What is the advantage of using Excel for data analysis?
  1. What precautions should you take to make accurate predictions?
  1. What is a function? Explain why the mathematical models that you found in this activity are functions.

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Introduction to Engineering DesignActivity 4.1c Mathematical Modeling– Page 1