Pregnant women metabolize some drugs at a slower rate than the rest of the population. The half-life of caffeine is about 4 hours for most people. In pregnant women, it is 10 hours1. (This is important because caffeine, like all psychoactive drugs, crosses the placenta to the fetus.) If a pregnant woman and her husband each have a cup of coffee containing 110 mg of caffeine at 8 am, how much caffeine does each have left in the body at 7 pm?

Husband:

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Woman:

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

Step-by-step explanation:

The amount of caffeine in the body can be modeled by the following equation:

In which C(t) is the amount of caffeine t hours after 8 am, C(0) is how much coffee they took and r is the rate the the amount of caffeine decreases in their bodies.

110 mg of caffeine at 8 am,

So

Husband

Half life of 4 hours. So

Applying ln to both sides

So for the husband

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Pregnant woman

Half life of 10 hours. So

Applying ln to both sides

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.