Chapter 4.2, Problem 20E

Reminder Round all answers to two decimal places unless otherwise indicated.

Decibels Sound exerts a pressure $P$ on the human ear. This pressure increases as the loudness of the sound increases. It is convenient to measure the loudness $D$ in decibels and the pressure $P$ in dynes per square centimeter. It has been found that each increase of $1\text{decibel}$ in loudness causes a $12.2\%$ increase in pressure. Furthermore, a sound of loudness $97\text{decibels}$ produces a pressure of $15$ dynes per square centimeter.

a.	Explain why $P$ is an exponential function of $D$ and find the growth factor.
b.	Find $P\left(0\right)$ and explain in practical terms what your answer means.
c.	Find an exponential model for $P$ as a function of $D$.
d.	When pressure on the ear reaches a level of about $200$ dynes per square centimeter, physical damage can occur. What decibel level should be considered dangerous?