meaning
Please say, which one from above is correct? If both of them are correct, please say the differences of meaning between them.
The big difference is that cumulative is far more common than accumulative.
At the level of actual meaning, to the extent that accumulative is used at all, it tends to refer to someone/something doing the accumulating. By contrast, cumulative is more associated with that which is accumulated.
If the sense intended is acquisitive, just use that word. In all other cases, use cumulative.
Whether they mean the same or not is easily ascertained:
[ODO]
ascribe verb [with object] (ascribe something to)
regard something as being due to (a cause):
he ascribed Jane’s short temper to her upset stomachattribute verb [with object] (attribute something to)
regard something as being caused by:
he attributed the firm’s success to the efforts of the managing director
his resignation was attributed to stress
Which "sounds more natural" is a subjective question, but Ngrams can provide some objective data. In your sentences I would use attributed to, which happens to match Google's data, but others may disagree.
Best Answer
Choice (2) is better. The use of "grow" in this context, while not technically wrong, is suspect since growing implies some sort of organic process that applies to individuals' adding more material to themselves. Vegetables grow, germinating from seeds in the earth. Children grow as they continue to eat. In this context, we're talking about a mere hike in numbers that applies to a collective, a "population," so the more neutral "increase" would be sufficient.
As a side note, I'm also not particularly fond of that hazy use of "with" and might recommend replacing with a clearer substitute, possibly "because of."