this table shows data collected by a runner. which statement about the scenario represented in the table is…

this table shows data collected by a runner. which statement about the scenario represented in the table is true? assume time is the independent variable.\n| time (minutes) | distance (miles) | elevation (meters) |\n| ---- | ---- | ---- |\n| 1 | 0.19 | 12 |\n| 2 | 0.38 | 26 |\n| 3 | 0.57 | 67 |\n| 4 | 0.76 | 98 |\n| 5 | 0.95 | 124 |\n| 6 | 1.14 | 145 |\nthe distance run is a nonlinear function because it does not have a constant rate of change.\nthe elevation is a nonlinear function because it does not have a constant rate of change.\nboth the distance run and the elevation are nonlinear functions because they do not have constant rates of change.\nboth the distance run and the elevation are linear functions because they have a constant rate of change.

this table shows data collected by a runner. which statement about the scenario represented in the table is true? assume time is the independent variable.\n| time (minutes) | distance (miles) | elevation (meters) |\n| ---- | ---- | ---- |\n| 1 | 0.19 | 12 |\n| 2 | 0.38 | 26 |\n| 3 | 0.57 | 67 |\n| 4 | 0.76 | 98 |\n| 5 | 0.95 | 124 |\n| 6 | 1.14 | 145 |\nthe distance run is a nonlinear function because it does not have a constant rate of change.\nthe elevation is a nonlinear function because it does not have a constant rate of change.\nboth the distance run and the elevation are nonlinear functions because they do not have constant rates of change.\nboth the distance run and the elevation are linear functions because they have a constant rate of change.

Answer

Explanation:

Step1: Check rate of change for distance

For distance, when time changes from 1 to 2 minutes, distance changes from 0.19 to 0.38 miles. Rate of change $=\frac{0.38 - 0.19}{2 - 1}=0.19$ miles per minute. When time changes from 2 to 3 minutes, distance changes from 0.38 to 0.57 miles. Rate of change $=\frac{0.57 - 0.38}{3 - 2}=0.19$ miles per minute. Since the rate of change of distance with respect to time is constant ($0.19$ miles per minute), distance is a linear function.

Step2: Check rate of change for elevation

When time changes from 1 to 2 minutes, elevation changes from 12 to 26 meters. Rate of change $=\frac{26 - 12}{2 - 1}=14$ meters per minute. When time changes from 2 to 3 minutes, elevation changes from 26 to 67 meters. Rate of change $=\frac{67 - 26}{3 - 2}=41$ meters per minute. Since the rate of change of elevation with respect to time is not constant, elevation is a nonlinear function.

Answer:

The elevation is a nonlinear function because it does not have a constant rate of change.