Question

the height of a rocket a given number of seconds after it is released is modeled by h(t) = -16t² + 32t + 15. what does t represent?
○ the number of seconds after the rocket is released
○ the initial height of the rocket
○ the initial velocity of the rocket
○ the height of the rocket after t seconds

Explanation:

The function \( h(t)= - 16t^{2}+32t + 15\) models the height of the rocket. In such a context, the variable \(t\) in the function's input represents the independent variable related to time. The problem statement says "a given number of seconds after it is released", so \(t\) should represent the number of seconds after the rocket is released. The initial height would be when \(t = 0\) (substituting \(t=0\) into the function gives \(h(0)=15\)), the initial velocity is related to the coefficient of the linear term (the derivative at \(t = 0\) for velocity in a quadratic height - time model), and \(h(t)\) is the height of the rocket after \(t\) seconds (the output of the function), not \(t\) itself.

Answer:

A. the number of seconds after the rocket is released