As others have stated, B-D are incorrect because we need to follow the idiom "so rapidly . . . that."
E uses "if" incorrectly. Any of the following would work:
"If the present rate continues, the global concentration will double."
"If the present rate continued, the global concentration would double."
"If the present rate were to continue, the global concentration would double."
Note that in the second and third examples, we are using a form of the past tense, followed by "would." Similarly, if we are going to say "If the rate did continue," we need to use "would" rather than "will."
The first example matches with A (the correct answer). "Should the present rate continue" is another way of saying "If the present rate continues." Many people aren't going to like this choice because this is a particular idiomatic use of the word "should" that's a little fancier than what we tend to use in everyday speech. This is exactly the kind of construction that the GMAT loves to use to throw us off the trail. If you are highly comfortable with written and spoken English, you are probably accustomed to this usage, but if not, you are left wondering what "should" is doing in there.
One last problem with E is that we don't really need to say "did continue." That usage is only needed if we are contradicting another idea:
"Country X has promised to stop polluting the ocean; however, if it did continue polluting, other countries would take actions against it."
I hope this helps!