Directions: Work these problems in your groups. Use Python to solve each problem. Answers

should be written in full sentences.

$1.$ Logarithms are used to help us process very small and very large numbers at the same time in an easy way. We measure things like magnitudes of earthquakes, noise levels in decibels, and pH levels of chemicals with logarithms. Decibels are measured as d $=10$ log $($P$/$P$0)$ where P is intensity of the sound being measured and P$0$ is the intensity of the weakest sound that the human ear can hear.

$($a$)$ Hearing someone breathing averages around $12$ decibels. Calculate the intensity of breathing noise relative to P$0.$

$($b$)$ A jet plane taking off is measure around $120$ decibels. Calculate the intensity of breathing noise relative to P$0.$

$($c$)$ We know that jet planes are not $10$ times louder than breathing, so calculate how many times more intense the jet engine noise is than breathing. Give the exact and approximate values.