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 -16^2 + 32t + 7. Kenny wants to know the height of the rock at 1 second after it leaves his hand, t = 1, and comes up with the answer 23 feet. How did Kenny find this result?

Question

A. Kenny substituted t= 1 into the expression -16 (1) (2) + 32 (1) + 7 = 23
B. Kenny substituted t= 7 into the expression -16 (7)^2 + 32 (7) + 7 = 23
C. Kenny substituted t= 23 into the expression -16 (23)^2 + 32 (23) + 7 = 23
D. Kenny sustetuded t= 1 into the expression -16 (1)^2 + 32 (1) + 7 = 23

Answer 1

To find the height of the rock at 1 second after it leaves Kenny's hand, we need to substitute \( t = 1 \) into the expression given for the height of the rock, which is:

\[ h(t) = -16t^2 + 32t + 7 \]

Now we substitute \( t = 1 \):

\[ h(1) = -16(1)^2 + 32(1) + 7 \] \[ = -16(1) + 32 + 7 \] \[ = -16 + 32 + 7 \] \[ = 16 + 7 \] \[ = 23 \]

Thus, Kenny arrives at the result of 23 feet by using the correct substitution into the expression.

The correct choice is:

D. Kenny substituted t= 1 into the expression -16 (1)^2 + 32 (1) + 7 = 23.