### Home > CALC > Chapter 3 > Lesson 3.2.1 > Problem 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)**0.0

2.0

3.1

6.0

7.5

9.0

**Distance (m)**0.0

3.8

9.1

32.7

49.7

69.5

Can Marquita use this table to determine her exact velocity at

*t*= 6. Explain.Approximate Marquita's velocity at

*t*= 6 using Hana' s method.Marquita' s teacher observed that her data fits the function

*d*(*t*) = 0.789*t*^{2}+ 0.703*t*− 0.338. Assuming that her teacher is correct, compute Marquita's*exact*velocity at*t*= 6 and*t*= 10.

Tables only give us select values of a function. What values are we given that are close to *t* = 6? Are these values close enough to find Marquita's exact velocity at *t* = 6?

Note: Since we do note know values that are infinitely close to *t* = 6, we can find Marquita's AROC (average velocity), not her IROC (actual velocity).

Use the Power Rule to find the IROC/derivative/slope function/velocity funciton.Then evaluate at *t* = 6 and again at *t* = 10.