11) The Half-Life of Tylenol is approximately 3 hours.
If you take 1000mg, how Tylenol much is left in your body after 4 hours?
The quantity remaining, r, from an initial quantity of r0 with a half life of h is given at time t by:
r=r0*e-t*ln(2)/h
For the given case,
initial quantity = 1000
half life, h = 3 hours
time lapse, t = 4 hours
so
r = 1000e-4ln(2)/3 mg
I'll let you finish the calculations because my calculator does not have the ln(x) function.
As a check of the formula, you can calculate the quantity left after 3 hours. It should be 500 mg.
To find out how much Tylenol is left in your body after 4 hours, you can use the formula for exponential decay:
Amount remaining = Initial amount * (1/2)^(time elapsed / half-life)
In this case, the initial amount is 1000mg and the half-life is 3 hours. We want to find the amount remaining after 4 hours.
Plugging the values into the formula:
Amount remaining = 1000mg * (1/2)^(4 / 3)
To simplify the calculation, we can transform the exponent using division:
Amount remaining = 1000mg * (1/2)^(4/3)
Now, we need to calculate 1/2 raised to the power of 4/3. To do this, we can take the cube root of 1/2 raised to the power of 4:
(1/2)^(4/3) = (√(1/2))^4
Taking the square root of 1/2:
√(1/2) = √1/√2 = 1/√2
Now, raising 1/√2 to the power of 4:
(1/√2)^4 = 1^4 / (√2)^4 = 1 / 2^2 = 1/4
Substituting this value back into the original formula:
Amount remaining = 1000mg * (1/4)
Simplifying the calculation:
Amount remaining = 1000mg / 4 = 250mg
After 4 hours, approximately 250mg of Tylenol will be left in your body.