The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.
The table shows the number of miles driven over time.
(4,204),(6,306),(8,408),(5,510)
To find the rate of change, we can look at the difference in miles driven and the difference in time for each consecutive pair of points in the table.
For the first pair of points (4,204) and (6,306), the difference in miles driven is 306 - 204 = 102 and the difference in time is 6 - 4 = 2.
For the second pair of points (6,306) and (8,408), the difference in miles driven is 408 - 306 = 102 and the difference in time is 8 - 6 = 2.
For the third pair of points (8,408) and (5,510), the difference in miles driven is 510 - 408 = 102 and the difference in time is 5 - 8 = -3.
The rate of change is the constant difference in miles driven for each unit change in time. In this case, the rate of change is 102 miles per 2 units of time, or 51 miles per unit of time.
This means that for every unit increase in time, the number of miles driven increases by 51.
To find the rate of change, we can compare the change in the number of miles driven to the corresponding change in time. Let's calculate the rate of change for each pair of points in the table:
For the first pair of points (4,204) and (6,306):
Change in miles driven = 306 - 204 = 102
Change in time = 6 - 4 = 2
Rate of change = Change in miles driven / Change in time = 102 / 2 = 51
For the second pair of points (6,306) and (8,408):
Change in miles driven = 408 - 306 = 102
Change in time = 8 - 6 = 2
Rate of change = Change in miles driven / Change in time = 102 / 2 = 51
For the third pair of points (8,408) and (5,510):
Change in miles driven = 510 - 408 = 102
Change in time = 5 - 8 = -3
Rate of change = Change in miles driven / Change in time = 102 / -3 = -34
The rate of change in the first two pairs of points is constant and equal to 51. However, for the third pair, the rate of change is -34, which indicates a decrease in the number of miles driven over time.
The rate of change represents the average amount of change in the number of miles driven for each unit of time. In this situation, a rate of change of 51 means that, on average, 51 miles are driven for each unit increase in time. The negative rate of change of -34 for the third pair indicates a decrease in the number of miles driven for each unit decrease in time.
To find the rate of change in a table, we need to examine the change in the dependent variable (in this case, the number of miles driven) for each unit change in the independent variable (in this case, time).
Let's calculate the rate of change between consecutive data points using the formula:
Rate of change = (Change in dependent variable) / (Change in independent variable)
In the given table:
(4,204),(6,306),(8,408),(5,510)
To find the rate of change between (4,204) and (6,306):
Change in dependent variable = 306 - 204 = 102
Change in independent variable = 6 - 4 = 2
Rate of change = 102 / 2 = 51
Similarly, we can find the rate of change between the other pairs of points:
Between (6,306) and (8,408):
Change in dependent variable = 408 - 306 = 102
Change in independent variable = 8 - 6 = 2
Rate of change = 102 / 2 = 51
Between (8,408) and (5,510):
Change in dependent variable = 510 - 408 = 102
Change in independent variable = 5 - 8 = -3
Rate of change = 102 / -3 = -34
The rate of change for this situation is 51 and -34, depending on the interval we consider. The positive rate of change (51) indicates that for every unit increase in time, there is an increase of 51 miles driven. Conversely, the negative rate of change (-34) indicates that for every unit decrease in time, there is a decrease of 34 miles driven.
In simple terms, the rate of change measures the speed or slope at which one variable changes with respect to another. It tells us how much one quantity is changing concerning another quantity. In this case, the rate of change represents how the number of miles driven is changing over time.