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 −16t2+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

Kenny found the height of the rock at 1 second after it leaves his hand by substituting \( t = 1 \) into the expression that models the height of the rock, which is given by \( -16t^2 + 32t + 7 \).

So, the correct response is:

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

Let's calculate it to confirm:

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

Thus, he correctly obtained 23 feet for the height of the rock at \( t = 1 \).