Question

A rock is thrown from one side of a river to another. The function h(t) = - 16t^2 + 80t + 30 gives the height in inches of the rock t seconds after it has been thrown.

1. Find h (4)
2. What does h (4) represent in the context of this problem?
3. Does it make sense to find h (-4) in the context of this problem?
4. What is a reasonable domain given the context of this problem?

a. 94
b. 16
c. 286
d. 4 seconds
e. The time it takes for the height to be 4 inches above ground
f. The height of the rock 4 seconds after it has been thrown.
g. The time it takes for the rock to hit the ground once it has been thrown
h. Yes, it makes sense because the height could be under sea level
i. No, it does not make sense because time cannot be negative
j. No, it does not make sense because we cannot have negative inches
k. A reasonable domain is all integers
l. A reasonable domain is all positive rational numbers
m. A reasonable domain is all positive irrational numbers

Answer 1

1. The height of the rock 4 seconds after it has been thrown can be found by substituting t=4 into the function h(t):

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.

2. In the context of this problem, h(4) represents the height of the rock 4 seconds after it has been thrown.

3. It does not make sense to find h(-4) in the context of this problem because time cannot be negative. Therefore, the answer is i. No, it does not make sense because time cannot be negative.

4. A reasonable domain given the context of this problem is all positive real numbers, since time cannot be negative in this context. Therefore, the answer is l. A reasonable domain is all positive rational numbers.