The height of a ball thrown upward from the ground is given by the quadratic function h = 120t - 16t2, where h is in feet and t is in seconds. what is the reasonable range for this function?

Given that the height of the ball has been modeled by h=120t-16t^2, the reasonable range will be found as follows:
maximum height is attained when h'(t)=0
given h=120t-16t^2
h'(t)=120-32t=0
thus solving for t, we get:
t=3.75 sec
thus the maximum time attained will be:
120(3.75)-16(3.75)^2=225 ft
Therefore the reasonable range will be [0≤h(t)≤225]

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