Question

Connor and Pilar are in a rock-climbing club. They are climbing dowa a canyon wall. Connor starts from a cliff that is 200 feet above the canyon floor and climbs down at an average speed of 10 feet per minute. Pilar climbs down the canyon wall as shown in the table.

Time (min 0 1 2 3
Pilars Height (ft) 242 234 226 218

Interpret the rates of change and initial values of the linear functions in terms of the situations that they model.

Answer 1

The rates of change represent the speeds at which Connor and Pilar are descending the canyon wall. Connor's rate of change is 10 feet per minute and Pilar's rate of change is -8 feet per minute. The initial values represent their starting heights: 200 feet for Connor and 242 feet for Pilar.

Step-by-step explanation:

The rates of change can be interpreted as the speeds at which Connor and Pilar are descending the canyon wall. Connor's rate of change, or his average speed, is 10 feet per minute. This means that he is climbing down at a speed of 10 feet for every minute that passes.

Pilar's rate of change can be calculated by finding the difference in her height at different times. Using the table, we can see that Pilar's height decreases by 8 feet every minute.

Therefore, Pilar's rate of change is -8 feet per minute.

The initial values of the linear functions represent the starting heights of Connor and Pilar. Connor starts from a cliff that is 200 feet above the canyon floor, so his initial value is 200. Pilar's initial height is given as 242 feet in the table, so her initial value is 242.