Wendy is playing with her new drone. After some time hovering at a fixed height above the ground, the drone begins descending at a constant rate.

Question

There is a linear relationship between the time, in seconds, since the drone started its descent, and the height of the drone, in feet.
Time (seconds) Height of drone (feet)
1 160
5 100
9 40
Describe the rate of change for this relationship.
The height of the drone
by
per second.

Answer 1

To describe the rate of change for the relationship between time and the height of the drone, we can calculate the slope of the line formed by the given points.

We have the following points from the data:

1. At \(t = 1\) second, the height is \(160\) feet.
2. At \(t = 5\) seconds, the height is \(100\) feet.
3. At \(t = 9\) seconds, the height is \(40\) feet.

Let's calculate the rate of change (slope) using the points (1, 160) and (9, 40).

The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Let's use points (1, 160) and (9, 40):

• \(y_1 = 160\), \(x_1 = 1\)
• \(y_2 = 40\), \(x_2 = 9\)

Now substituting the values into the slope formula:

\[ m = \frac{40 - 160}{9 - 1} = \frac{-120}{8} = -15 \]

This result indicates that the height of the drone decreases by \(15\) feet per second.

Therefore, the height of the drone decreases by 15 feet per second.