1.2 Rate of Change
Specific Outcome:
M.1 ‐ Solve problems that involve the application of rates. [CN, PS, R]
Miss Andersen is preparing to bake cookies. She pre­heats the oven to 350oF.
The graph shown represents the temperature of an oven as it warms up.
a) What does the point (0, 50) on the graph represent?
Oven Temp. (oF)
(4, 350)
b) What does the point (4, 350) on the graph represent?
(0, 50)
Time (min)
c) Calculate the slope of the line joining these two points.
rate of change
d) The slope represents a ______________________. What units are used to represent this?
e) The temperature is _____________________ at the rate of _________ __________ per _________.
(increasing/decreasing)
rate of change
**Recall: Slope represents a ____________________________.
­A rate of change can be used to describe many scenarios distance vs. time, temp. vs. time, salary vs. sales
i.e.) _______________________________________________________
positive rate of change
­positive slope = ______________________________
negative rate of change
negative slope = _________________________________
average speed between two points
­In the case of distance vs. time, slope = __________________________
Examples
1. Larry entered his car in a long distance car race. He travelled the first 150 km in 2 hours. After 6 hours he had travelled 650 km.
a) Plot the ordered pairs to represent this information. Explain why (0, 0) is included as an ordered pair in this scenario.
b) Calculate Larry's average speed between 2 hours and 6 hours. Is this considered a rate of change?
c) By looking at the grid and without doing any calculations, how can we tell that the average speed during the first 2 hours was less than the average speed during the next 4 hours?
The following graph represents the amount of fuel in Larry's gas tank as a function of the distance travelled during a portion of the race where he drove at a constant speed.
d) Calculate the slope of the line.
# of Litres in Fuel Tank
( N)
(20, 50)
(120, 40)
Distance in km (d)
e) Describe this rate of change.
Examples
2. Millie leaves her house to go for a ride on her scooter. The diagram illustrates the amount of fuel she has in her tank as a function of time.
Describe a scenario involving rate of change which could be represented by the graph.
Amount of Fuel in Tank (L)
Time (min)
p. 19 #s 1 ­ 8
­Quiz Tomorrow!!
­Please bring a ruler tomorrow
Exit Slip:
The following graph represents a rate of change with units oC/s. Explain why.
Temp.
(oC)
Time (s)