Question

14. Michael is walking from home to a subway stop that is 10 blocks away. Calculate Michael's average rate of
change, in blocks per minute, for each of the following intervals:

Answer 1

The rate of change of Michael within the given ranges are constant.

• $\displaystyle The \ average \ rate \ of \ change \ from \ \mathbf{0} \ to \ \mathbf{ 9 }\ minutes \ is \ \underline{\frac{1}{3} \ blocks/minute}$

• The average rate of change from 9 to 13 minutes is 1 block per minute

• $\displaystyle The \ average \ rate \ of \ change \ from \ \mathbf{13} \ to \ \mathbf{19} \ minutes \ is \ \underline{\frac{1}{2} \ blocks/minute}$

Reasons:

The likely points on the graph as obtained from a similar question online are;

(0, 0), (6, 2) (9, 3), (11, 5), (13, 7), (15, 8), (19, 10)

Required:

The average rate of change from 0 to 9 minutes.

Solution:

$\displaystyle Rate \ of \ change = \frac{3 \ blocks - 0 \ blockes}{9 \ minutes - 0 \ minutes } = \mathbf{\frac{1}{3} \ blocks/minute}$

$\displaystyle The \ average \ rate \ of \ change \ from \ 0 \ to \ 9 \ minutes \ = \underline{\frac{1}{3} \ blocks/minute}$

Required:

The average rate of change from 9 to 13 minutes.

Solution:

$\displaystyle 9 \ to \ 13 \ minutes = \frac{7 \ blocks - 3 \ blocks}{13 \ minutes - 9 \ minutes } = \frac{4}{4} \ blocks/minute = 1 \ blocks/minute$

The average rate of change from 9 to 13 minutes = 1 block per minute

Required:

The average rate of change from 13 to 19 minutes.

Solution:

$\displaystyle 13 \ to \ 19 \ minutes = \frac{10 \ blocks - 7 \ blocks}{19 \ minutes - 13 \ minutes } = \frac{3}{6} \ blocks/minute = \frac{1}{2} \ blocks/minute$

$\displaystyle The \ average \ rate \ of \ change \ from \ 13 \ to \ 19 \ minutes \ = \underline{\frac{1}{2} \ blocks/minute}$

Learn more about rate of change of a graph here:

https://brainly.com/question/13672531