Let's say the charge on the battery is 1000000. I just picked that number off the top of my head for the sake of the argument, so don't think about it too much. But, if it loses 1% power, it's now at 900000. Then it loses 1% again, but it's 1% of 900000, so now it's at 810000. 99% of that number is 729000. 99% of that number is 654100. It's losing 1% of the current (full) charge each day, so it's losing less each day.
In other words, on the second day it loses 1% of the original charge, leaving 99%. On the third day, it loses 1% of (99% of the original charge). On the fourth, it loses 1% of (99% of 99% of the original charge). The mathematical function for this is:
(original charge) x .99^x (that means .99 to the power of the number of days). That's called exponential decay. Since the loss is smaller as the result gets smaller, mathematically speaking, it will never reach zero (though, obviously in the real world a battery stops being useful long before it reaches fractions of a minute of charge). If it lost 1% of the original maximum charge every day, that would be linear decay because it's the same change every day, and then it would be useless in 100 days.
With a linear decay at the rate of 1% a day, however, after a hundred days, the maximum charge is a little more than a third of the original (36.6%). A hundred days later, it's a third of that. So you see, there's a big difference between linear and exponential decay.
Of course, if Kingfield is right (I have no idea how a lithium battery acts, I'm just going on what Fat D said), it'll last much longer than that.
In other words, on the second day it loses 1% of the original charge, leaving 99%. On the third day, it loses 1% of (99% of the original charge). On the fourth, it loses 1% of (99% of 99% of the original charge). The mathematical function for this is:
(original charge) x .99^x (that means .99 to the power of the number of days). That's called exponential decay. Since the loss is smaller as the result gets smaller, mathematically speaking, it will never reach zero (though, obviously in the real world a battery stops being useful long before it reaches fractions of a minute of charge). If it lost 1% of the original maximum charge every day, that would be linear decay because it's the same change every day, and then it would be useless in 100 days.
With a linear decay at the rate of 1% a day, however, after a hundred days, the maximum charge is a little more than a third of the original (36.6%). A hundred days later, it's a third of that. So you see, there's a big difference between linear and exponential decay.
Of course, if Kingfield is right (I have no idea how a lithium battery acts, I'm just going on what Fat D said), it'll last much longer than that.
