[eglaud]

So I have an answer key that says the order, from least to greatest, of Germanium, Silicon, and Carbon's electron affinities, with the answer being below
 
Smallest numeric value (most favorable, releases E) C < Si < Ge


But this doesn't follow the periodic trends we've learned, plus looking it up the opposite is found.

So wouldn't carbon have the largest electron affinity, then silicon, then germanium? Or am I misreading this?

[Enthalpy]

http://www.webelements.com/periodicity/electron_affinity/
+154 kJ/mol Carbon
+134 kJ/mol Silicon
+119 kJ/mol Germanium

[mikasaur]

http://study.com/academy/lesson/electron-affinity-definition-trends-equation.html

Perhaps you're (or your book is) confusing EA with the energy change associated with taking on an electron. EA is defined as:

EA = -ΔE

The -154 kJ/mol ΔE for Carbon is certainly a "lower" number than -134 kJ/mol ΔE for Silicon. This may be why the answer is the opposite of what you understand it to be.