a. The drone's descent can be modeled by a linear function because it is descending at a constant rate, which means that the change in height over time is consistent.
b. The rate of change of the drone's height is negative, as it is descending towards the ground. This means that the value of the linear function (i.e., the height of the drone) is decreasing as time passes.
c. To find the equation that models the drone's descent as time increases, we need to use the two pieces of information given in the problem: that the drone hovers at 16 meters for a few minutes before descending, and that it reaches the ground after 6 seconds.
Let's define the linear function as h(t), where h represents the height of the drone and t represents the time elapsed since the drone started descending.
We know that the drone hovers at 16 meters for a few minutes, so we can say that h(t) = 16 for t < t0, where t0 is the time when the drone starts descending.
Once the drone starts descending, we know that it takes 6 seconds to reach the ground, so we can write:
h(t) = 16 - rt, where r is the rate of descent (in meters per second).
To find r, we can use the fact that the drone reaches the ground after 6 seconds. This means that when t = 6, h(t) = 0:
0 = 16 - r(6)
Solving for r, we get:
r = 16/6 = 2.67
Therefore, the equation that models the drone's descent as time increases is:
h(t) = 16 - 2.67t, for t ≥ t0.