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

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  −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=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=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 1 2 plus 32 times 1 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

GPT-4o mini · Answer

Kenny found the height of the rock at $ t = 1 $ second by substituting $ t = 1 $ into the expression for the height of the rock. The correct response is: **Kenny substituted $ t = 1 $ into the expression $ -16(1)^2 + 32(1) + 7 = 23 $** This leads to the calculation: $$ -16(1)^2 + 32(1) + 7 = -16(1) + 32 + 7 = -16 + 32 + 7 = 16 + 7 = 23 $$ Thus, the height of the rock at 1 second after it leaves his hand is indeed 23 feet.