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

Question

seconds can be modeled by the expression −16t^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?

(1 point)
Responses

Kenny substituted t=23
into the expression −16(23)^2+32(23)+7=23
Kenny substituted t is equal to 23 into the expression negative 16 times 23 squared plus 32 times 23 plus 7 is equal to 23

Kenny substituted t=1
into the expression −16(1)^2+32(1)+7=23
Kenny substituted t is equal to 1 into the expression negative 16 times 1 squared plus 32 times 1 plus 7 is equal to 23

Kenny substituted t=7
into the expression −16(7)^2+32(7)+7=23
Kenny substituted t is equal to 7 into the expression negative 16 times 7 squared plus 32 times 7 plus 7 is equal to 23

Kenny substituted t=1
into the expression −16(1)(2)+32(1)+7=23

Answer 1

The correct response is:

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

This means that to find the height of the rock at 1 second after it leaves his hand, Kenny substituted \( t = 1 \) into the height equation:

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

Thus, the height of the rock at \( t = 1 \) second is indeed 23 feet.