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3-47.

After completing the Ramp Lab in Chapter 2, Marquita decided to ride her bicycle down a nearby hill to gain more data on rolling objects. The data she collected is shown in the table below. Homework Help ✎

Time (sec)

Distance (m)

  1. Can Marquita use this table to determine her exact velocity at  Explain.

    Tables only give us select values of a function. What values are we given that are close to ? Are these values close enough to find Marquita's exact velocity at ?

  2. Approximate Marquita’s velocity at using Hana’s method.

    Hanna’s Method:  where represents the value whose slope you are looking for.

    Note: Since we do note know values that are infinitely close to , we can find Marquita's AROC (average velocity), not her IROC (actual velocity).

  3. Marquita’s teacher observed that her data fits the function . Assuming that her teacher is correct, compute Marquita’s exact velocities at  and .

    Use the Power Rule to find the IROC/derivative/slope function/velocity function. Then evaluate at  and again at .