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EXAMPLE 4 Solve a multi-step problem 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. Space Exploration

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

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

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

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

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GUIDED PRACTICE for Example 4 Use a graphing calculator to find a polynomial function that fits the data. 5. y = 2.71x 3 – 25.5x 2 + 71.8x – 45.7 ANSWER

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GUIDED PRACTICE for Example 4 6. ANSWER y = – 0.587x 3 + 8.99x 2 – 23.4x + 9.62

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EXAMPLE 3 Model with finite differences

EXAMPLE 3 Model with finite differences

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