**Transcription of Image for Educational Website:**---### Question 11A person's lung capacity can be modeled by the function $ C(t) = 250 \sin \left( \frac{2 \pi t}{5} \right) + 2450 $, where $ C(t) $ represents the volume in mL present in the lungs after $ t $ seconds. State the maximum value of this function over one full cycle, and explain what this value represents.**Input Section:** [Type your response here or upload a picture here]---**Explanation:**In this mathematical model, the function $ C(t) $ describes how the lung capacity or the volume of air in the lungs varies over time, measured in milliseconds (mL) and seconds (t). The function is specifically a sinusoidal function, which often represents periodic phenomena like breathing.**Function Breakdown:**- **Base Function:** $ C(t) = 250 \sin \left( \frac{2 \pi t}{5} \right) $ - This part of the function has an amplitude of 250 mL, frequency coefficient of $ \frac{2 \pi}{5} $ indicating the cyclic nature of breathing.- **Vertical Shift:** $ + 2450 $ - This means the entire sinusoidal wave is shifted up by 2450 mL.**Maximum Value:**The sine function, $ \sin(\theta) $, oscillates between -1 and 1. Thus, the maximum value of $ \sin \left( \frac{2 \pi t}{5} \right) $ is 1.- When $ \sin \left( \frac{2 \pi t}{5} \right) = 1 $: \[ C_{\max}(t) = 250 \times 1 + 2450 = 250 + 2450 = 2700 \text{ mL} \]**Interpretation:**The maximum value of 2700 mL represents the highest volume of air that the lungs can hold at any point during a breathing cycle. This suggests the peak or maximum lung capacity in this model is 2700 mL.

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A person's lung capacity can be modeled by the function C(t) = 250sin(t) + 2450, where C(t) represents the volume in mL present in the lungs aftert seconds. State the maximum value of this function over one full cycle, and explain what this value represents. Type your response here or upload a picture here

A person's lung capacity can be modeled by the function C(t) = 250sin(t) + 2450, where C(t) represents the volume in mL present in the lungs aftert seconds. State the maximum value of this function over one full cycle, and explain what this value represents. Type your response here or upload a picture here

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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