The population of the world is increasing very fast.
(Why it does not use 'increases'?)
- At first I didn't like my job, but I'm beginning to enjoy it now.
(Why it does not use 'I begin'?)
3a. You can turn off the radio, I don't listen to it.
3b. You can turn off the radio, I'm not listening to it.
Which sentence is correct?
The present continuous construction is used to emphasise an action happening now. We can think of now as being different from (- as contrasting with) usually, habitually, generally or always.
When we talk about actions that happen usually, or always, we use the present simple:
- I play the violin
- I smoke
- I work in London
If you see a man jumping up and down, and you ask him: "What do you do?". His answer will be something like "I am a teacher". He won't say "Jumping up and down". This is because you used a present simple form for the question. Therefore he is telling you what he does usually. If you ask him "What are you doing?", then that means "What are you doing NOW", because you used a present continuous form. He will say "I'm jumping up and down".
Of course, some things that we usually do, we are also doing right now too. When we choose the present simple or continuous, it sometimes just shows how we are thinking. For example, if you see a man fall off a building, you might ask "Is he breathing?". You know that he usually breathes! But you are interested in if he is breathing NOW!.
In sentence (1) the speaker is emphasizing that the increase in world population is happening at the moment. This makes it seem more dramatic. It also seems to make us think that the population didn't use to increase so fast (although it doesn't say this). If we say:
- The population of the world increases very fast.
This means it increases very fast all the time, or usually.
In sentence (2) the speaker has to use a continuous verb form, because we can't usually begin the same thing all the time!
In sentence (3a), the speaker never listens to the radio. So it doesn't matter if you turn it off. Maybe somebody different turned it on!
In sentence (3b), however, the speaker is just saying that they aren't listening to it NOW. Maybe they listen to it a lot. But at this moment they aren't. So you can turn it off.
Both of the sentences in (3) are correct. But they mean different things.
Note: The present continuous doesn't necessarily mean the action is happening 'this second'. But it does mean that we are thinking about the action as in progress at the moment, as opposed to happening usually. For example, I can say I'm reading Romeo and Juliet at the moment. This doesn't mean this second but it means I am currently in the middle of reading it. This still contrasts with reading it all the time, or regularly: I read Shakespeare means I read Shakespeare regularly.
Hope this is helpful!