Rate of Change
Task 1: Definition
1. What is rate of change?
2. Give a real example of a positive rate of change and another with a negative rate
of change.
Task 2: Situations
1. A hot air balloon rose from a height of 100 m to 400 m in 3 minutes.
What was the balloon’s rate of change?
2. A glacier advanced down a mountain from an elevation of
2010 m in 1995 to 1780 m in 2000. What was the glacier’s rate
of change per year?
3. A sky diver falls 100 meters in 10 seconds. Calculate the rate of
change.
4. Jim paid a sum of $34.25 for 6 pairs of socks. What is the price
of one sock?
Task 3:
1)
Students Number of
Textbooks
5
15
10
30
15
45
20
60
a) Describe how the number of students changes the number of textbooks..
b) Do you think the relation above is linear? Explain your thinking.
2)
x
3
4
5
6
y
75
100
100 125
150
a) Give a real life situation where the data given in the above table is applied.
b) Find the rate of change and describe it.
3) If you know that the rate of change is 58 miles per hour, find the distances covered
for the given times.
Time (hours)
4
6
8
10
Distance (miles)
Task 4:
You work for a video streaming company that has two monthly plans for customers to
choose from:
Plan 1: A rate of $2.50 per video viewed plus $7 fixed for each month
Plan 2: $4 per video viewed
a. What type of relations are represented in these two plans?
b. Write an equation that relates total cost to videos viewed for each monthly plan.
c. Make a table for plan A and another for plan B showing the cost of watching 0, 3,
5, 8 videos in a month.
d. What is the rate of change of each?
e. Graph the two equations on the same coordinate system and label each (Use
appropriate scales according to your table values).
f. Compare the two plans graphically and explain what advice you would give to a
customer trying to decide which plan is best for them, based on their viewing habits.