Question

Niklas takes a dose of 25 micrograms of a certain supplement each day. The supplement has a half life of 4 hours, meaning that 1/64 of the supplement remains in the body after each day. How much of the supplement is in Niklas's body immediately after the 12th dose? Round your final answer to the nearest hundredth.

Answer 1

The amount of the supplement in Niklas' body immediately after the 12th dose is 4.30 micrograms.

Explanation:

Half life is the time required for an element to decay into half of its initial size. The supplement has a half life of 4 hours means that it decay to half of its size every 4 hours. Therefore there are 6 stages of division in a day.

i.e
`(1)/(2)` ×
`(1)/(2)` ×
`(1)/(2)` ×
`(1)/(2)` ×
`(1)/(2)` ×
`(1)/(2)` =
`(1)/(64)`

The amount of the supplement in Niklas' body after the first dose (first day) can be determined by;

=
`(1)/(64)` × 25

= 0.390625 micrograms

He used the supplement daily for 12 days (12th dose), but the amount of the supplement in his body immediately after the 12th dose would be;

amount in his body per day × number of period for complete decay

= 0.390625 × 11

= 4.296875

The amount of the supplement in Niklas' body immediately after the 12th dose is 4.30 micrograms. This is because immediately after the 12th dose, the supplement has not reach its half life.