Word Thinking Question

Question

Etienne finds it difficult to sleep if he has too much caffeine in his system when he goes to bed at 11 pm. He has one cup of coffee at 9:00 am. He likes to have a second cup of coffee later in the day. What is the latest time he can have a second cup of coffee and still fall sleep at 11 PM if:

a) he can’t have more than 50mg of caffeine in his system

b) he can’t have more than 25mg of caffeine in his system

Some assumptions:

Etienne consumes no other caffeine during the day.

The half life of caffeine in his system is 5.5 hours.

An average cup of coffee has 125 MG of caffeine.

Use the same model equation througout your solution

Answer 1

The half-life of a drug is the amount of time it takes for the drug's concentration in the body to decrease by half. So, consuming a 125 mg cup of coffee at 9am means that there will be 62.5 of caffeine left in the body still at 2:30pm, and 31.26 mg at 8pm.

We start at 11pm with 50mg of caffeine in his body, and want to find out how long it will take, going backwards in time, to get to 125mg, which is one cup of coffee.

The formula to use for half-lives is logarithmic.

Time= (half-life) log 1/2 (drug concentration at time / initial drug concentration)

T= (5.5) log 1/2 (50/125)

=7.27 hours

Your last cup of coffee should be had by 3:44 pm in order to have no more than 50mg of caffeine in his body at 11pm.