Can someone explain to me how a $99 computer can have 45ghz of processing power, but an i7 costs 3x that for 1/10th that clock speed? What does this $99 miss out on that my i7 has the capability of doing?
First of all, this 45GHz figure definitely isn't valid for modern x86 chips - thanks to multiple cores and SIMD instructions they reach few dozen GFLOPS at stock frequencies.
Furthermore, x86 chips pack all of their performance in low number of cores, what makes them much more useful for common scalar code. And if 20 times higher scalar performance isn't enough to convince you to pay premium, the complexity required to achieve this level of scalar performance definitely is enough to discourage Intel from selling you i7s for $99.
This is kind of a novelty. Your i7 has way, way more power for jobs which only use a few cores. Most normal jobs are like that, so unless you have specific requirements, the i7 is going to give you much better performance.