A half-life of 168 hours

Every figure on this page is a function of one number: 168 hours. Five of those is 35 days, and down to one percent takes about 1116 hours. No compound is named here and none is implied.

Educational arithmetic only. Not medical advice and not a dosing protocol.

Whole multiples of a 168-hour half-life. The percentage column is exact: one half to the power n is a rational number and is computed as one, so these figures are not rounded decimals.
Half-lives elapsed	Remaining, exactly	Elapsed	Which is
1	50.0000%	168 hours	7 days
2	25.0000%	336 hours	14 days
3	12.5000%	504 hours	21 days
4	6.2500%	672 hours	28 days
5	3.1250%	840 hours	35 days
6	1.5625%	1008 hours	42 days
7	0.7813%	1176 hours	49 days

Clock time to five remaining fractions. These are approximate: the exponent is fractional except at whole multiples of the half-life, so the value is irrational and is rounded for display.
To	Remaining	Hours, about	Which is about
Down to a half	50%	168.0 hours	7 days
Down to a quarter	25%	336.0 hours	14 days
Down to a tenth	10%	558.1 hours	23 days 6.1 hours
Down to a twentieth	5.0%	726.1 hours	30 days 6.1 hours
Down to a hundredth	1.0%	1116.2 hours	46 days 12.2 hours

A 168-hour half-life against seven intervals. The interval is a parameter in this table and nothing more: no row is a suggestion, and the second column is the only thing that determines the rest of the row.
Interval	Intervals per half-life	Surviving the gap	Limit the peaks approach	Intervals to within 1%
8 hours	0.05	96.8%	30.80x	140
12 hours	0.07	95.2%	20.70x	94
24 hours	0.14	90.6%	10.61x	47
48 hours	0.29	82.0%	5.57x	24
72 hours	0.43	74.3%	3.89x	16
168 hours	1.00	50.0%	2.00x	7
336 hours	2.00	25.0%	1.33x	4

What this figure is not

This is educational arithmetic on figures entered by the reader. It is not medical advice, not a dosing protocol, and not a recommendation that anything be prepared, obtained or administered.

Nothing here states what quantity is appropriate for anyone, and there is no function in it that produces an amount to administer. A question about anyone’s health belongs with a licensed clinician who can examine the person asking.

Compounds of the kind this arithmetic is used on are largely research chemicals that are not approved by the FDA for human use. An exact calculation is not an accurate measurement: what is actually in a syringe depends on the preparation and the device, neither of which this page can see.

A half-life belongs to the population, formulation and route it was measured in. Carrying one anywhere else is an assumption rather than a calculation, and this site holds no half-life for any compound: the figure is whatever was typed into the form.

An interval on this site is a parameter, never a proposal. No page here suggests how often anything should happen, and a geometric series evaluated at a spacing somebody chose is not a schedule.

No qualified clinical reviewer is recorded against this site, and no credential is claimed anywhere on it. the full version.

What is particular to this half-life

A week, which makes the weekly column of the table below the clean case: ratio exactly one, half surviving, limit exactly 2 - the same arithmetic as the 24-hour page at a 24-hour interval, on a different clock. The eight-hour column is the other extreme on this site, with a limit above twenty.

Reading the third table

The second column is the whole story. It is the interval divided by the half-life, and it is the only input to the three columns after it: the fraction surviving a gap is 0.5 to that power, and the limit is one over one minus that fraction. Two rows with the same figure in column two have identical arithmetic however different the clock times are.

At a 168-hour half-life and a 24-hour interval, 0.14 half-lives pass between repeats, about 90.6% of one amount survives the gap, and the peaks approach about 10.61 times one amount after roughly 47 intervals. Every one of those four figures comes from the ratio and from nothing else.

Why the first table is exact and the other two are not

At whole multiples of a half-life the exponent is a whole number, so the remaining fraction is exactly one half to the power n - a rational number, computed as one. That is why the first table has figures like 3.1250% in it rather than 3.13%.

Everywhere else the exponent is fractional and the value is irrational. There is no exact decimal to print, so those tables are computed in floating point and labelled approximate. Exact and approximate sets out which figures across this whole site are which, and why the distinction is worth making rather than papering over.

What this page is not

It is not about a compound. No substance has a 168-hour half-life as far as this page is concerned; 168 hours is a number, chosen as one of ten points spanning the range this arithmetic is useful over. A published half-life belongs to the species, formulation, route and assay that measured it, and this site holds no such figure for anything.

It is also not a schedule. The intervals in the third table are parameters swept across a plausible range so that the shape of the function is visible. None of them is a proposal, and what this does not do is explicit about that.

Elsewhere on this site

The worksheetAny half-life and any interval, rather than the seven tabulated here.
The other nine half-life valuesSame three tables, a different number at the top.
The same grid by intervalHold the interval fixed and sweep the half-life instead.