Question

Leonard drinks coffee that contains 300 mg of caffeine. Over the course of the day, every hour, one-half of the caffeine in his system leaves the body and one-half stays. Let x = the number of hours and y = the amount of caffeine in Leonard's system. If he finishes his coffee at 9:00 am, how many mg of caffeine are left in his system at 1:00 pm? Write the equation using the variables above that represents this situation and solve the problem, showing the calculation you did to get your answer.

Answer 1

18.75 mg

Explanation:

We can model this problem using the exponencial equation:

y = yo * (1 + r)^x

Where y is the final value, yo is the inicial value, r is the rate and x is the amount of time.

In this problem, we want to find y after x = 4 hours (from 9am to 1pm), we have yo = 300 and r = -0.5 (for every hour, half the caffeine leaves the body). So we have that:

y = 300 * (1 - 0.5)^4

y = 300 * 0.5^4

y = 300 * 0.0625

y = 18.75 mg