The amount of pain relievers in your system after x hours can be determined using an exponential decay function.
The general form of an exponential decay function is:
y = a * e^(-kx)
where:
- y is the amount of pain relievers in your system after x hours
- a is the initial amount of pain relievers in your system
- k is the decay constant
To find the specific function for this situation, we can use the information given in the problem.
We know that the initial amount of pain relievers in your system is 400mg, so a = 400. We also know that there are only 71mg left in your system after 4 hours, so we can use this information to find the decay constant, k.
We can use the formula:
y = a * e^(-kx)
71 = 400 * e^(-k * 4)
Dividing both sides by 400, we get:
0.1775 = e^(-4k)
Taking the natural logarithm of both sides, we get:
ln(0.1775) = -4k
Solving for k, we get:
k = ln(0.1775) / -4
k ≈ 0.245
So the specific function for this situation is:
y = 400 * e^(-0.245x)
where x is the number of hours since you took the pain reliever.