The Problem:

When we use x-rays to take pictures of the human body the transmission coefficient in our exponential model depends on the type of x-ray we're using. Soft x-rays are less damaging but are more strongly absorbed while hard x-rays penetrate better while having greater health effects. These differences are what we are exploring in this model N=N₀e^{λ x}.

The data for the attenuation coefficients (λ in our model) is given at the end of this page. Here is the executive summary. For soft x-rays λ is 0.4 1/cm for bone and 0.043 1/cm for muscle. For hard x-rays λ is 0.06 1/cm for bone and 0.03 1/cm for muscle.

Assume that the leg being x-ray'd has 2 cm of bone and 12 cm of muscle that we are trying to distinguish. Calculate the intensity of x-rays that make it though the bone and the muscle in each case (you will get 4 numbers). You may assume that the initial intensity of the x-rays is 100 "lumens".

Based on the numbers you have calculated does it make more sense to you to use hard or soft x-rays for this purpose? Explain your answer clearly.