FL 5, PS 26

The explanation doesn't make sense to me. I'm confused about how the negative sign was removed. By my calculation, the final answer will be e to the negative 1.

But im guessing the real answer may have to do with the nature of e and logs. Is there a way you can explain that pls?
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This question reads:  “What is the ratio of the intensity of an X-ray beam after it passes through 1 cm of plasma to the intensity of the beam after it passes through 6 cm of plasma?  (Note:  Plasma has an absorption coefficient of approximately 0.2 cm^-1.”

The first thing we notice is that the answer choices all include e… we’ll need natural logs or equations with e in them.  Do we know any?  Probably not.  But they give us an equation in the passage:  I = I₀e^-μx, where I is the intensity after passing through the medium, I₀ is the original intensity, μ is the absorption coefficient, and x is the distance traveled.

The ratio asks for I_{1 cm}/1_{6 cm}.  We should already have an idea that the intensity at 1 cm is higher than 6 cm (since it gets less intense as it passes through the medium).  We’re already down to (C) and (D) then.  Let’s do the math.

I_{1 cm}  = I₀e^{-μ(1 cm)}

I_{6 cm}  = I₀e^{-μ(6 cm)}

Plugging in, I_{1 cm}/1_{6 cm} = I₀e^{-(0.2)(1 cm)}/ I₀e^{-(0.2)(6 cm)}

Let’s get rid of the constant I₀ to make this easier…

e^-0.2/e^-1.2 = e^{-0.2 – (-1.2)} = e¹ = e.

So the ratio is e/1, or answer choice (C).

If you kept getting e^-1, make sure that you noticed the negative sign before μ in the equation; that might have been what messed you up.