I don't understand constant rate of change can you give me some examples.
The graph I have shows the depth of the water in a vase over 8 days
constant rate of change.
constant speed is constant change of distance/time
so if you are going 25mph, your distance is changing at a constant 25miles each hour.
Certainly! Constant rate of change is a concept used in mathematics to describe how quickly or slowly a quantity changes over time. It measures how much a value changes in relation to another value, usually represented as a ratio or fraction. In the context of your graph showing the depth of water in a vase over 8 days, we can see if there is a constant rate of change by examining the relationship between the days and the corresponding depth of water.
To determine the constant rate of change, you can select any two points on the graph and calculate the difference in the depth of water between those two points. Then divide the change in depth by the number of days between the two points to find the rate of change. If the rate of change is the same for every pair of points, then there is a constant rate of change.
Let's consider an example to make it clearer. Suppose we have the following data for the depth of water in the vase:
Day 1: 10 cm
Day 2: 8 cm
Day 3: 6 cm
Day 4: 4 cm
Day 5: 2 cm
Day 6: 0 cm
Day 7: -2 cm
Day 8: -4 cm
To determine the constant rate of change, we can choose two points such as Day 1 and Day 4. The change in depth between Day 1 and Day 4 is 10 cm - 4 cm = 6 cm. The number of days between the two points is 4 - 1 = 3 days. Therefore, the rate of change is 6 cm / 3 days = 2 cm/day.
If we repeat the process for other pairs of points, we find that the rate of change is consistently 2 cm/day. This indicates that the depth of the water in the vase is decreasing by 2 centimeters each day, showing a constant rate of change.
I hope this example helps you understand the concept of constant rate of change. If you have any further questions, feel free to ask!