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

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

GPT-4o mini · Answer

To find the height of the rock at $ t = 1 $ second, we need to substitute $ t = 1 $ into the height equation. The height of the rock is given by the expression: $$ h(t) = -16t^2 + 32t + 7 $$ Now, substituting $ t = 1 $: $$ h(1) = -16(1)^2 + 32(1) + 7 $$ Calculating each term: 1. $ -16(1)^2 = -16 $ 2. $ 32(1) = 32 $ 3. The constant is $ 7 $ Combining these values gives: $$ h(1) = -16 + 32 + 7 = 16 + 7 = 23 $$ Thus, Kenny found that the height of the rock at $ t = 1 $ is indeed 23 feet. The correct choice from the options is: **D. Kenny substituted $ t = 1 $ into the expression $ -16(1)^2 + 32(1) + 7 = 23$**.