Terms referring to rate of change
are common in descriptions of various
phenomena and processes. For example, the rate of
growth of a country's population is an important
figure that must be taken into account when
planning for the future.
Follow the
Population clock,
for a few minutes and watch the US government's continuously updated estimate of US and world populations. How do the US and world populations change
each minute? What about each day? Can you predict the world's population a
year from today?
This activity focuses on ways in which the rate of change of
processes is expressed when the processes are described
mathematically, using functions.
|
The tool below helps you choose a rate of
change (displayed graphically in the upper window)
and examine the graph of the resulting function
(displayed graphically in the lower window, when
you press the graph button).
In this way, you can construct different functions
with different types of change.
|
|
|
|
How is the rate of change expressed in different representations of a function?
|
|
Use the tool above to display functions that change in various
ways: increasing or decreasing at a constant rate, increasing or
decreasing at an increasing rate, increasing or decreasing at a
decreasing rate. Record the graphs that you obtained.
|
|
|
What properties characterize the graphs with a constant rate of change?
|
|
|
Use the Change at a constant rate
tool to display different functions: increasing, decreasing, and constant.
Describe these functions in various representations and state how the
rate of change is expressed in different representations: value tables, graphs, and correspondence rules.
|
|
|
Write stories or describe phenomena that can be
represented using a linear function, and explain how
the rate of change is expressed in the phenomena
you describe.
|
|
|
|
|
|
