Using $H(t)=10+8\sin(\pi t/6)$, what height is predicted at $t=4.7$ minutes, to the nearest tenth?

Answer and derivation

Correct answer: B

$H(4.7)\approx15.034$, so the predicted height is 15.0 meters.

1. Substitute 4.7 into the time variable.
2. In radian mode, evaluate $10+8\sin(4.7\pi/6)$.
3. Round once at the end to 15.0 meters.

Why the other options fail

A

At $t=4.7$, $8\sin(4.7\pi/6)\approx5.0346$, so adding the midline gives 15.0 m, not 12.0 m. Degree mode would give about 10.3 m; it does not explain this option.

B

In radians, $H(4.7)=10+8\sin(4.7\pi/6)\approx15.0346$. Rounding only the final height to the nearest tenth gives 15.0 m.

C

The maximum is 18 m at 3 minutes, but being near that time does not justify 17.9 m. Evaluating the model at 4.7 minutes gives 15.0 m.

D

Since $-1\le\sin(\pi t/6)\le1$, the model satisfies $2\le H(t)\le18$. A height of 20.0 m is outside its range.

Common misconception: Trigonometric model inputs inherit the angle unit encoded in the coefficient.

China/AP bridge: China-course bridge: substitution is familiar; AP newly expects students to support a contextual prediction with mode, units, and precision; unlike copying a display, state meters and rounding; a common pitfall is degree mode or missing parentheses.