Kenny is standing on top of a boulder at his neighborhood pond. He picks up a small rock, so that it is 7 feet off the ground, and throws the rock into the pond. The height of the rock after t seconds can be modeled by the expression −16t^2+32t+7. What does 7 represent in the context of the problem?

Question

Kenny is standing on top of a boulder at his neighborhood pond. He picks up a small rock, so that it is 7 feet off the ground, and throws the rock into the pond. The height of the rock after t seconds can be modeled by the expression −16t^2+32t+7. What does 7 represent in the context of the problem?
A) 7 represents the number of seconds Kenny hold the rock before throwing it.
B) 7 represents the number of rocks Kenny found at the pond.
C) 7 represents the height of the rock when Kenny throws it.
D) 7 does not make sense as a value in this problem.

GPT-4o mini · Answer

In the context of the problem, the expression \(-16t^2 + 32t + 7\) models the height of the rock after \(t\) seconds, where the term \(7\) represents the initial height of the rock at the moment when it is thrown (which is 7 feet off the ground). Therefore, the correct answer is:

C) 7 represents the height of the rock when Kenny throws it.