a helicopter that is 200 meters above the ground descends at a rate of 2 meters per second. The altitude of the helicopter after t seconds is given by h(t)=2000-2t.
1)give the range of this function
2)give the domain of this function.
1. 0 less than or equal to t less than or equal to 1000
2. 0 less than or equal to h(t) less than or equal to 2000
1) To find the range of the function h(t), we need to determine the set of all possible values that the function can output. In this case, the altitude of the helicopter is given by the expression h(t) = 2000 - 2t, where t represents time in seconds.
Since the helicopter starts at an altitude of 200 meters and descends at a rate of 2 meters per second, we know that the altitude is decreasing with time. Therefore, the minimum possible value for h(t) will occur when the time, t, is at its maximum value. To find this maximum value, we need to consider when the helicopter reaches the ground, which occurs when h(t) = 0.
Setting h(t) = 0 and solving for t:
0 = 2000 - 2t
2t = 2000
t = 1000
So, it takes 1000 seconds for the helicopter to reach the ground. Therefore, the range of the function h(t) is given by the set of possible altitudes: h(t) ∈ [0, 200].
2) The domain of the function h(t) is the set of possible input values, in this case, the values of t. Since time can be any positive real number, the domain of h(t) is t ∈ (0, ∞).