the correct statement is: b. The elevation is a nonlinear function because it does not have a constant rate of change.
To determine whether the distance run and the elevation are linear or nonlinear functions, let's examine the rates of change for each.
Distance Run:
- The change in distance for each unit increase in time is constant (0.19, 0.38, 0.57, ...).
- The rate of change is constant, indicating a linear relationship between time and distance.
Elevation:
- The change in elevation for each unit increase in time is not constant (12, 28, 39, ...).
- The rate of change is not constant, indicating a nonlinear relationship between time and elevation.
Therefore, the correct statement is:
b. The elevation is a nonlinear function because it does not have a constant rate of change.
The probable question may be:
"This table shows data collected by a runner.
A three column table with 7 rows. The first column, Time in minutes, has the entries, 1, 2, 3, 4, 5, 6. The second column, Distance in miles, has the entries, 0.19, 0.38, 0.57, 0.76, 0.95, 1.14. The third column, Elevation in meters, has the entries, 12, 28, 67, 98, 124, 145.
Which statement about the scenario represented in the table is true? Assume time is the independent variable.
a. The distance run is a nonlinear function because it does not have a constant rate of change.
b The elevation is a nonlinear function because it does not have a constant rate of change.
c. Both the distance run and the elevation are nonlinear functions because they do not have constant rates of change.
d. Both the distance run and the elevation are linear functions because they have a constant rate of change."