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**1. Homework Statement**

In this lab various thicknesses of a few materials are placed between a source of gamma radiation and a couple different detectors. It is reasonable to assume that some small change in the thickness of the shielding would produce a proportional change in the intensity of the gamma rays measured on the other side. If we define

*I*to be the incident intensity of the gamma rays upon the shielding slab of thickness

*ΔX*, and the emerging intensity on the other side of the shielding to be

*I*’ with proportionality constant

*µ*, we can describe the hypothesis with the simple model:

__(Δ__= -

*I*)*μΔX*

*I*

According to the lab manual the solution to the integration of this equation yields

*I*=

*I0e^(-μx) ; Where*

*I0 is the incident intensity***3. The Attempt at a Solution**

So for an infinitesimally small change delta, we would use the Latin '

*d'*giving

I

__dI__= -*μdX*I

integrating both sides and exponentiating then yields

*I*= e^(-

*μX)*

So where does the term

*I0*come from? Can someone show me where my error is?