Question

Please help me ASAP

Answer 1

We have the function for the height:

`h(t)=-16t^2+36t+96`

The average rate of change between t=2 and t=4 can be calculated as:

`\begin{gathered} r=(h(4)-h(2))/(4-2) \\ r=((-16\cdot4^2+36\cdot4+96)-(-16\cdot2^2+36\cdot2+96))/(2) \\ r=(-16(4^2-2^2)+36(4-2))/(2) \\ r=(-16(16-4)+36\cdot2)/(2) \\ r=(-16\cdot12+72)/(2) \\ r=(-192+72)/(2) \\ r=-(120)/(2) \\ r=-60 \end{gathered}`

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.