Questions:

1. Which of the following does not represent a situation that involves an average rate of change? Explain your answer.

a) A child grows 7 cm in 6 months.

b) A jogger ran 25 km in 2 hours.

c) A plane travelled 550 km in 3 hours.

d) The average height of the basketball players is 1.9 m.

e) The room temperature decreased by 3⁰C over one week.

2. The height, h, in metres, of a ball above the ground after t seconds can be modeled by the function h(t) = -3.8t² + 10t.

a) What does the average rate of change represent for this situation?

b) Determine the average rate of change of the height of the ball for each time interval.

i) (1, 3)

ii) (1, 1.2)

iii) (1, 1.5)

iv) (1, 1.01)

v) (1, 1.001)

c) Compare the values in part b). Describe their relationship.

3. A soccer ball is kicked into the air such that its height, h, in metres after t seconds can be modeled by the function h(t) = -2.8t² + 10t + 0.5.

a) Determine the average rate of change of the height of the ball from 1s to 2s.

b) Estimate the instantaneous rate of change of the height of the ball after 1s.

c) Sketch the curve and the tangent.

d) Explain the average rate of change and the instantaneous rate of change in this situation.