Question

6 mark for review interval (in seconds) 0 to 6 6 to 12 12 to 18 18 to 24 24 to 30 drone a +17 -4 +11 -5 -3 drone b +5 +3 +3 +2 +3 two drones are flying over a given area, and their heights above the ground are changing. the table gives the change in height, in feet, for the drones over successive 6 - second intervals. which of the following is true about the average rates of change for drone a and drone b over the time interval from t = 0 seconds to t = 30 seconds? a the average rates of change are equal. b the average rate of change for drone a is greater than for drone b. c the average rate of change for drone b is greater than for drone a. d the average rates of change cannot be determined because changes in heights are given, not heights of the drones.

Explanation:

Step1: Calculate total change for Drone A

Add up the height - changes for Drone A: $17+( - 4)+11+( - 5)+( - 3)=17 - 4+11 - 5 - 3 = 16$.

Step2: Calculate total change for Drone B

Add up the height - changes for Drone B: $5 + 3+3+2+3=16$.

Step3: Calculate average rate of change

The time interval is from $t = 0$ to $t = 30$ seconds, so $\Delta t=30$ seconds. The average rate of change is $\frac{\text{total change}}{\text{total time}}$. For both drones, the total change is 16 and the total time is 30 seconds. So the average rates of change are equal.

Answer:

A. The average rates of change are equal.