A.4.7.3 Populations of Two States
- Author:
- LeonMilewski
The graphs show the populations of California and Texas over time.
1.
a. Estimate the average rate of change in the population in each state between 1970 and 2010. Show your reasoning.
b. In this situation, what does each rate of change mean?
2. Which state’s population grew more quickly between 1900 and 2000? Show your reasoning.
Discuss questions such as:
- “How would you explain average rate of change to a classmate who is absent today? What does it tell us? How do we find it?”
- “Which representation—a table or a graph—can give us a better sense of the general trend of a function over a certain interval? Why?” (A graph, because we can visualize a line that fits the data in an interval and reason about its slope.)
- “What does a negative average rate of change tell us?” (The output of the function is decreasing for every unit of increase in input.)
- “If a function has a negative average rate of change over an interval, does it mean that the function value never increases?” (No, there might be parts of the interval where the function value rises, but overall, it is falling.)
- “When dealing with Mai and Tyler’s case, we compared average rates of change over two intervals that are not the same length. Was that a fair comparison? Does the length of the interval matter?” (Yes, it is a fair comparison. The length of the interval doesn’t matter because an average rate of change gives the amount of change per unit of input.)