A rock is thrown from one side of a river to another. The function h(t) = −16t2 + 80t + 30 gives the height in inches of the rock t seconds after it has been thrown.

Question

Find h(4)

What does h(4) represent in the context of this problem?

Does it make sense to find h(-4) in the context of this problem?

What is a reasonable domain given the context of this problem?

Answer 1

To find h(4), substitute t = 4 into the function h(t) = -16t^2 + 80t + 30:

h(4) = -16(4)^2 + 80(4) + 30
h(4) = -16(16) + 320 + 30
h(4) = -256 + 320 + 30
h(4) = 94

Therefore, h(4) = 94. In the context of this problem, h(4) represents the height in inches of the rock 4 seconds after it has been thrown.

It does not make sense to find h(-4) in the context of this problem because time cannot be negative in this scenario.

A reasonable domain for this problem would be all non-negative real numbers, since time cannot be negative and the function represents the height of the rock at any given time after being thrown. So the domain would be t ≥ 0.