4) Rebecca is flying a drone at a constant height. She decides to make the drone rise vertically. It rises 18 m every 3 s . After 5 s , the drone is at a height of 40 m . The drone's height in meters, \( y \), is a function of the time in seconds, \( x \). (4)) How many meters does the drone rise each second? Find the rate of change. 4) 6 meters per second 4) What is the height of the drone before Rebecca makes it rise? Find the initial value. (4)

Let's break down the problem step by step. ### Step 1: Determine the rate of change (rise per second) Rebecca's drone rises 18 meters in 3 seconds. To find the rate of change (rise per second), we can use the formula: \[ \text{Rate of change} = \frac{\text{Rise}}{\text{Time}} = \frac{18 \, \text{m}}{3 \, \text{s}} \] Calculating this gives: \[ \text{Rate of change} = 6 \, \text{m/s} \] ### Step 2: Find the initial height of the drone We know that after 5 seconds, the drone is at a height of 40 meters. Since the drone rises at a rate of 6 meters per second, we can calculate how much it has risen in those 5 seconds: \[ \text{Height increase} = \text{Rate of change} \times \text{Time} = 6 \, \text{m/s} \times 5 \, \text{s} = 30 \, \text{m} \] Now, to find the initial height before Rebecca makes the drone rise, we subtract the height increase from the final height: \[ \text{Initial height} = \text{Final height} - \text{Height increase} = 40 \, \text{m} - 30 \, \text{m} = 10 \, \text{m} \] ### Summary of Results 1. The drone rises **6 meters per second**. 2. The initial height of the drone before it starts rising is **10 meters**.