An item is being lifted by an elevator at a constant speed to a height of 10 feet. The item does not move for five seconds then catapults off the 10-foot platform and back to the ground. Compare the height of the item to the time passed in seconds. Determine the correct types of functions that describes the scenario in the correct order.
The scenario can be divided into two parts: the item being lifted by the elevator and the item catapulting off the 10-foot platform.
1. The item being lifted by the elevator:
- Height of the item in relation to time: This can be described by a constant function because the item is being lifted at a constant speed. The height remains constant at 10 feet during this part of the scenario. Therefore, the function that describes the height of the item during this time is h(t) = 10, where h(t) represents the height of the item at time t.
2. The item catapulting off the 10-foot platform:
- Height of the item in relation to time: This can be described by a quadratic function because the height of the item will change continuously as time passes. As the item catapults off the 10-foot platform, it will follow a parabolic path. Therefore, the function that describes the height of the item during this time is h(t) = -16t^2 + 10, where h(t) represents the height of the item at time t. The term "-16t^2" represents the effect of gravity on the height, and the constant term "10" represents the initial height of the item.
In summary, the correct types of functions that describe the scenario in the correct order are:
1. Constant function: h(t) = 10
2. Quadratic function: h(t) = -16t^2 + 10