Wikipedia: Half-life describes the time it takes for the blood plasma concentration of a substance to halve its steady-state.
First, does this imply that the blood plasma concentration of a drug decrease exponentially? Secondly, what can be said about the change in activity/effectiveness of the drug by time? (I know SSRIs may work long after the drug is off the body)
The concentration of drugs declines based on a property of the specific drug called pharmacokinetics. Here's a broad-brush strokes overview (more info here):
A drug with zero order kinetics declines linearly. This is often the case if a drug is metabolized by an organ such as the liver. Alcohol has 0-order kinetics. If your blood alcohol level is 0.8 at midnight, it might be 0.6 at 1AM, 0.4 at 2AM, 0.2 at 3AM, and 0.0 at 4AM.
A drug with first order kinetics declines exponentially. This is common in drugs that are excreted from the kidney. Say you have a drug level of 0.8 at midnight. At 1AM it might be 0.4, then 0.2 at 2AM, then 0.1 at 3AM, then 0.05 at 4AM. It will continue to decline exponentially until there is an undetectable amount of drug in the body.
As to your second point (more info here):
Most drugs work based on plasma concentration. Take an antibiotic: if the plasma concentration is too low, it isn't able to have an effect (killing bacteria), simple as that.
Some drugs, however, cause longer-term changes in the body. This is especially common with psychoactive drugs such as SSRIs. The effect of these drugs is to cause the body to produce more receptors to the neurotransmitter serotonin. This takes several weeks to occur, and also takes several weeks (or months) to reverse. In this way, the effect of the drug can be seen long after the drug is stopped.
