Answer:
I will give you the link below to a PDF that one of my young friends made for someone who had this exact question.
Step-by-step explanation:
The appropriate domain for this situation is [tex]\{t : 0 \leq t \leq 1.5\ \& \: t \in \mathbb R \}[/tex] (that means t can be any real number and between 0 and 1.5 (both endpoints included)
Domain is the set of values for which the given function is defined.
Range is the set of all values which the given function can output.
For this case, we have only those values of 't' as appropriate value, which are from t = 0 till the time when ball hits the ground, since after that the height will be constantly 0, but the height function will give negative values which doesn't model the situation correctly.
Thus, those values of t for which the equation [tex]h(t) = -16t^2 + 24t[/tex] correctly models the real world situation are said to be appropriate values of domain of this function.
The time when the ball will reach the ground will be when the height will be 0, thus,:
[tex]0 = -16t^2 + 24t\\2t^2 - 3t = 0\\(2t-3)(t) = 0\\t = 0, t = 3/2 = 1.5 \: \rm sec[/tex]
The height is 0 when ball starts going up(t=0), and when t = 1.5 the ball reaches ground.
Thus, the appropriate domain for modelling the situation is values of t in the interval [0, 1.5] (both endpoints are inclusive, as shown by big bracket).
Learn more about appropriate domain here:
https://brainly.com/question/2510516
