Final answer:
The function that models the elevation of the hot air balloon is H(x) = 6x + 90. The domain of the function is all real numbers, and the range is all real numbers greater than or equal to 90.
Step-by-step explanation:
The function that models the elevation of the hot air balloon is given by H(x) = 6x + 90, where x represents the time since you first noticed the hot air balloon. In this function, x is the input variable and H(x) represents the height of the balloon at time x. The domain of the function is all real numbers since time can be any positive or negative value. The range of the function is all real numbers greater than or equal to 90, since the height of the balloon starts at 90 meters and increases as time passes.