Background
Four explanations that would otherwise have to appear on three worksheets each. Derivations and definitions, with every figure in them checkable by hand.
Educational arithmetic only. Not medical advice and not a dosing protocol.
- What a half-life isThe definition, and the four things attached to a published figure that get dropped when it is quoted.
- Where the series comes fromThe accumulation derivation in four lines, and what each line assumes.
- Exact and approximateWhich figures on this site are exact, which are bounds, and which are floating point.
- Vial yield is a divisionThree ways to misread the simplest arithmetic here, and what the worksheet does about each.
What makes something a background page rather than a worksheet
A worksheet takes figures and returns figures. A background page explains why a worksheet behaves the way it does, and earns a page only when the same explanation would otherwise be repeated. There are four of them and the site is small on purpose.
None of these pages asserts anything about a compound, a preparation or a body. Two of them derive formulae, one describes the behaviour of floating-point arithmetic, and one is about an off-by-one. All four can be checked by anyone with a pencil.
The thread running through all four
Each is about the boundary of what the arithmetic can claim. The half-life page is about a parameter whose provenance the site cannot see. The series page is about a model with four assumptions in it. The exactness page is about three different kinds of guarantee being printed in the same typeface. And the division page is about a correct count that still does not mean what it looks like.
Getting the maths reliably right removes one category of error from a situation that has several. These four pages are about the ones that remain.