We have the function for the height:
[tex]h(t)=-16t^2+36t+96[/tex]The average rate of change between t=2 and t=4 can be calculated as:
[tex]\begin{gathered} r=\frac{h(4)-h(2)}{4-2} \\ r=\frac{(-16\cdot4^2+36\cdot4+96)-(-16\cdot2^2+36\cdot2+96)}{2} \\ r=\frac{-16(4^2-2^2)+36(4-2)}{2} \\ r=\frac{-16(16-4)+36\cdot2}{2} \\ r=\frac{-16\cdot12+72}{2} \\ r=\frac{-192+72}{2} \\ r=-\frac{120}{2} \\ r=-60 \end{gathered}[/tex]The units of the rate of change are the units of height (feet) divided by the units for time (seconds), so the rate of change is -60 feet/second.
Answer: Between 2 and 4 seconds, the height decreases at an average rate of 60 feet per second.