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.
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:
Let assume that Earth is a sphere, the following trigonometric diagram is constructed and presented below. The central angle is given by this inverse trigonometric equation:
The distance of the portion of Earth that can be seen is:
