1. The problem is to analyze the function $h(t) = 9.25 \sin[0.2(t - 2.5)] + 12.25$. 2. This is a sinusoidal function of the form $h(t) = A \sin(B(t - C)) + D$, where: - $A = 9.25$ is the amplitude, which determines the height of the wave peaks from the midline. - $B = 0.2$ affects the period of the sine wave. - $C = 2.5$ is the horizontal phase shift, shifting the graph to the right by 2.5 units. - $D = 12.25$ is the vertical shift, moving the midline up by 12.25 units. 3. The period $T$ of the sine function is given by the formula: $$T = \frac{2\pi}{B} = \frac{2\pi}{0.2} = 10\pi \approx 31.42$$ 4. The amplitude $A = 9.25$ means the function oscillates 9.25 units above and below the midline $y = 12.25$. 5. Therefore, the maximum value of $h(t)$ is: $$12.25 + 9.25 = 21.5$$ 6. The minimum value of $h(t)$ is: $$12.25 - 9.25 = 3$$ 7. The phase shift $C = 2.5$ shifts the sine wave to the right by 2.5 units along the $t$-axis. 8. In summary, $h(t) = 9.25 \sin[0.2(t - 2.5)] + 12.25$ is a sinusoidal function with amplitude 9.25, period approximately 31.42, phase shift 2.5, and vertical shift 12.25. This function is valid and correctly written for modeling periodic phenomena with these parameters.