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?

Answer 1

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.