Question

Caffeine decreases in your bloodstream at a rate of 12% per hour. If you drink 2 cans of Red Bull (111 mg each), how many hours will it take for your caffeine level to drop to 10 mg?

Answer 1

To find out how many hours it will take for the caffeine level from 2 cans of Red Bull to decrease to 10 mg, we use the exponential decay formula and logarithms to solve for time.

Step-by-step explanation:

This involves a mathematical understanding of exponential decay to determine how many hours it will take for the caffeine level in the bloodstream to drop below a certain level. You initially ingest 2 cans of Red Bull, each containing 111 mg of caffeine, adding up to 222 mg. To find out how long it will take for this to decrease to 10 mg in your bloodstream, you can use the formula for exponential decay: C(t) = C0 × (1 - r)^t. where C(t) is the caffeine concentration at time t, C0 is the initial concentration, r is the decay rate per hour, and t is time in hours. Plugging in the values we get: 10 = 222 × (1 - 0.12)^t. Solving for t involves using logarithms: t = log(10/222) / log(1 - 0.12). After performing the calculations, you will get the number of hours required for the caffeine to decrease to 10 mg.