The difficulty of generating bitcoins increases exponentially over time
No, it changes in proportion to the number of blocks generated in the past week or two. This could even result in a decrease if the number of miners decrease.
.. really? Interesting! Thank you for the correction, I've been reading enough about BTC while considering mining and this is the first time I've heard this.
The difficulty is adjusted every 2016 blocks based on the time it took to find the previous 2016 blocks. At the desired rate of one block each 10 minutes, 2016 blocks would take exactly two weeks to find. If the previous 2016 blocks took more than two weeks to find, the difficulty is reduced. If they took less than two weeks, the difficulty is increased. The change in difficulty is in proportion to the amount of time over or under two weeks the previous 2016 blocks took to find.
No, it changes in proportion to the number of blocks generated in the past week or two. This could even result in a decrease if the number of miners decrease.