The half-life of a medication prescribed by a doctor is 6 hours. How many mg of this medication is left after 78 hours if the doctor prescribed 100 mg?
To calculate the half-life of a medication, we can use the formula:
Amount remaining = Initial amount × (1/2)^(t/h)
where:
- Amount remaining is the amount of medication left after a certain period of time
- Initial amount is the original amount of medication prescribed by the doctor
- t is the time that has passed
- h is the half-life of the medication
Given:
Initial amount = 100 mg
t = 78 hours
h = 6 hours
Using the formula:
Amount remaining = 100 × (1/2)^(78/6)
First, let's simplify the exponent:
78/6 = 13
Now let's calculate the amount remaining:
Amount remaining = 100 × (1/2)^13
Using a calculator or by performing the calculation step by step:
Amount remaining ≈ 100 × 0.0195
Amount remaining ≈ 1.95 mg
After 78 hours, approximately 1.95 mg of the medication is left.
To determine the amount of medication left after 78 hours, we can use the half-life formula:
Amount remaining = Initial amount * (1/2)^(time elapsed / half-life)
Given:
Initial amount = 100 mg
Half-life = 6 hours
Let's substitute these values into the formula and calculate the amount remaining after 78 hours:
Amount remaining = 100 mg * (1/2)^(78 / 6)
Now, let's simplify this expression:
Amount remaining = 100 mg * (1/2)^(13)
To compute (1/2)^13, we can use a calculator:
(1/2)^13 = 0.0001220703125
Now, substitute this value back into the original equation:
Amount remaining = 100 mg * 0.0001220703125
Calculating the expression:
Amount remaining = 0.01220703125 mg
Therefore, after 78 hours, there would be approximately 0.0122 mg of the medication left.