How Does Caffeine Decrease in Your Bloodstream Over Time?

[HelloMotto]

I'm having trouble with this question.

The percent "P", of caffeine remaining in your bloodstream is related to the elapsed time, "t', in hours, by t = 5(log P/ log 0.5)

a) How long will it take for the amount of caffeine to drop to 25% of the amount consumed?

b) Suppose you drink a cup of coffee after dinner at 5:00 pm. What % of the caffeine will remain in your system when you go to bed at 10:30 pm.

 

[Tedjn]

a) What would P be if the caffeine in your blood stream is now 25% of the original amount consumed?

b) What variable, t or P, do you know in this case? How would you solve for the other one?

 

[Architeuthis Dux]

I would suggest approaching this problem by first understanding the equation provided. The equation given, t = 5(log P/ log 0.5), is a logarithmic function that relates the elapsed time (t) to the percentage of caffeine remaining in the bloodstream (P). The base of the logarithm is 0.5, which indicates that the percentage of caffeine remaining will decrease by half every 5 hours.

To answer the first question, we can plug in the given information of P = 25% and solve for t. This would give us t = 5(log 25/ log 0.5) = 15 hours. Therefore, it would take 15 hours for the amount of caffeine to drop to 25% of the amount consumed.

For the second question, we can use the given information of drinking a cup of coffee at 5:00 pm and going to bed at 10:30 pm to find the percentage of caffeine remaining at 10:30 pm. We first need to find the elapsed time between 5:00 pm and 10:30 pm, which is 5.5 hours. We can then plug this value into the equation as t = 5.5 and solve for P. This would give us P = 12.5%, meaning that approximately 12.5% of the caffeine consumed will still be in the bloodstream at 10:30 pm.

In summary, understanding the given equation and using basic algebraic techniques can help us answer these questions and gain a better understanding of the relationship between time and percentage of caffeine remaining in the bloodstream. It is important to approach scientific problems with a clear understanding of the given information and utilizing appropriate mathematical tools to arrive at a solution.