Rates of Changename:Period

Rates of ChangeName:Period:

1) A big storm knocked out the power in Jonathon’s house and his cell phone is dead! He only has one candle that he can burn to light his room until his parents get home. Jonathon read the packaging for the candle and found that it is supposed to lose 4cm of height every hour.

Jonathon started a table to make some predictions about the candle.

x / Hours / 0 / 1 / 2
y / Height of candle (cm) / 20 / 16

Use the information from the story to finish the table andgraph the points.

a) What is the starting height of the candle? ______This is called the initial value. Highlight this value on the table and on the graph. What are the coordinates? ( , )

b) The candle’s height is changing at a rate of –4 cm per hour. How is this shown on the table?

How is thisrate of change shown on the graph? (Brainstorm as a team!)

c) Jonathon’s parents will be home in four hours. How tall will the candle be when they get home? ___

Circle where you could find this information on both the table and the graph.

d) Jonathon lit the candle at 7:12 pm. At what time should it burn out completely? How do you know?

2) Lydia is writing a story for the city paper on the city bicycle race. She noticed that Racer #5 is so highly-trained that it looks like he rides at a constant speed throughout the entire main part of the race. She drew a distance-over-time graph of his progress through the part of the race that she watched (on the back of this paper).

She got called away on another assignment for the city paperand left so quickly that she couldn’t fill her editor in on Racer #5. She left the editorial team her graph and now they have to write the story!

Your team is the editorial team at the paper. You must analyze the graph to recover as much information as possible. You are particularly interested in his speed (rate).

What information did your team gather about Racer #5 and his alarmingly consistent rate? How far was he when Lydia started watching?

a) There was a disagreement within the editorial team regarding Racer #5 ‘s rate. Here are the different rates that the editorial team came up with:

1) 11 km every 6 minutesJustify:

2) 15 km every 12 minutes

3) 5 km every 4 minutes

4) 2 km every 3 minutes

5) 20 km every 20 minutes

Which rate is right? Circle the correct one and justify.

b) If Lydia watched for 24 minutes, what would Racer #5’s distance have been?

c) The main part of the race that Lydia was watching is 35 km long. How many minutes would Lydia have needed to watch to see him get to this distance?

3) a) A rate is a ratio that compares two related quantities. For example, 27 cents per 5 ounces or 70 miles per 2 gallons. Write a rate for Jonathon’s situation and one for Lydia’s situation:

Johnathon’s rate: Lydia’s rate:

b) How the coordinates (points) change on a line can be expressed as a rate of change and this shows how the y-values change compared to the x-values. Rates of change are written as difference in y-values per difference in x-values.

The rate of changebetween coordinates (points) can be expressed as a fraction in this form:

For the examples in part (a): and

Write the rates of change you found for Jonathon and Lydia as simplified fractions. Johnathon: Lydia:

c) Write a rate of change for the situation below: Remember rate of change is difference in y per difference in x.

Rate of change: