To solve this problem, we need to understand the significance of evaluating [tex]\( h(t) \)[/tex] at [tex]\( t = 3.2 \)[/tex].
The function [tex]\( h(t) = -16 t^2 + 28 t + 500 \)[/tex] represents the height of a rock [tex]\( t \)[/tex] seconds after it is propelled by a slingshot.
When we substitute [tex]\( t = 3.2 \)[/tex] into this function, we are calculating the height of the rock 3.2 seconds after it is launched. Specifically:
[tex]\[ h(3.2) \][/tex]
This calculation gives us the height of the rock at that specific time.
After performing the calculation, we find that:
[tex]\[ h(3.2) = 425.76 \][/tex]
This means that 3.2 seconds after the rock is propelled, its height is 425.76 meters. Therefore, [tex]\( h(3.2) \)[/tex] represents:
The height of the rock 3.2 seconds after it is propelled.
