Final answer:
a. The x-values represent minutes because the problem states the time elapsed during the drive. b. The rate of change is calculated using the slope formula and is equal to 120 feet per minute. c. Devin will gain 1800 feet in the next 15 minutes if he continues to climb at the same rate.
Step-by-step explanation:
a. The x-values should represent minutes because the problem states that Devin drove for a certain amount of time in minutes and the elevations are given in feet. The x-values indicate the time elapsed during Devin's drive.
b. To calculate the rate of change, we can use the formula:
Rate of change = (change in y-values) / (change in x-values)
Using the given data:
Rate of change = (1580 - 620) / (12 - 4) = 960 / 8 = 120 feet per minute
The method used is the slope formula, where the rate of change represents the slope of the line between the two points.
c. If Devin continues to climb at the same rate, we can calculate the elevation he will gain in the next 15 minutes by multiplying the rate of change by the time:
Elevation gained = Rate of change * Time
Elevation gained = 120 feet per minute * 15 minutes = 1800 feet
Devin will gain 1800 feet in the next 15 minutes.