I don't think the story is about caffeination, but rather caffeine as a marker of human waste. 45 nanograms per liter doesn't sound like a lot, especially when considering the short half life of caffeine.
The biological half-life of caffeine (how long it takes the human body to eliminate it) is not important here; it's not about humans but the sea life; nobody knows what happens to marine life in a continuous exposure to traces of caffeine and other substances.
If we assume 100 mg in a cup of coffee, we can do the math by: 1.010E^(-1)/4.510E^(-8)
which is equal to 2.22*10E^(6) or 2.22M liters of water. You're only off by a factor of 370!
Since one cubic meter is 1000 liters, you're looking at a cubic body of water that is 13 meters or ~40ft on each side.
It's reasonable to assume that "x * 10E^(y)" was meant as a notation for "x * 10^(y)" = "xEy", but many mathematical notations are overloaded. I have no way of knowing whether GP was genuinely confused, or merely trying to point out the nonstandard usage, but I prefer to believe the former.
Simple way to visualize this: Think about the difference between a 4-foot square and 4 square feet. The former is a much bigger area.
But the thing is - it's 45 ng/l in the whole environment around sea organisms.
I don't know if that's a large dose or not, I'm just saying the half-life comment doesn't seem to apply in this case.