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Polynomial Model for Space Shuttle Speed in Ft/s

This text provides a polynomial model for the speed of a space shuttle during launch, and uses this model to predict when the shuttle's speed reaches 4400 ft/s.

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Polynomial Model for Space Shuttle Speed in Ft/s

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  1. Space Exploration The table shows the typical speed y(in feet per second) of a space shuttle x seconds after launch. Find a polynomial model for the data. Use the model to predict the time when the shuttle’s speed reaches 4400 feet per second, at which point its booster rockets detach. EXAMPLE 4 Solve a multi-step problem

  2. STEP 1 Enter the data into a graphing calculator and make a scatter plot. The points suggest a cubic model. EXAMPLE 4 Solve a multi-step problem SOLUTION

  3. EXAMPLE 4 Solve a multi-step problem STEP 2 Use cubic regression to obtain this polynomial model: y = 0.00650x3– 0.739x2 + 49.0x – 236

  4. EXAMPLE 4 Solve a multi-step problem STEP 3Check the model by graphing it and the data in the same viewing window.

  5. The booster rockets detach about 106 seconds after launch. EXAMPLE 4 Solve a multi-step problem STEP 4Graph the model and y = 4400 in the same viewing window. Use the intersect feature.

  6. Use a graphing calculator to find a polynomial function that fits the data. 5. ANSWER y = 2.71x3 – 25.5x2 + 71.8x – 45.7 for Example 4 GUIDED PRACTICE

  7. 6. ANSWER y = – 0.587x3 + 8.99x2 – 23.4x + 9.62 for Example 4 GUIDED PRACTICE

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