Final answer:
It will take approximately 26.9 hours until there is less than 15 mg of caffeine left in Mohammed's bloodstream.
Step-by-step explanation:
The half-life of caffeine is approximately 5 hours. To calculate the time it takes for there to be less than 15 mg of caffeine left in Mohammed's bloodstream, we can use the equation:
C(t) = C0 * (1/2)^(t/h)
where C(t) is the concentration of caffeine at time t, C0 is the initial concentration of caffeine (350 mg), t is the time passed, and h is the half-life of caffeine (5 hours).
Let's solve for t:
15 = 350 * (1/2)^(t/5)
Dividing both sides by 350:
0.042857 = (1/2)^(t/5)
Taking the logarithm of both sides:
log(0.042857) = log[(1/2)^(t/5)]
Using the logarithmic property, we can bring t/5 down:
log(0.042857) = (t/5) * log(1/2)
Dividing both sides by log(1/2):
t/5 = log(0.042857) / log(1/2)
Multiply both sides by 5:
t = 5 * (log(0.042857) / log(1/2))
Plugging this into a calculator, the value for t is approximately 26.9 hours.