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&[DATE] &[TIME] - &[FILENAME]

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

Evolution of alcoholic intoxication

This document does not deal about "drinkers myths". "There is no harm in getting hammered if you do it now and them". 1. C(a,t) => cumulative integral from Maple call. 2. R(a,t) => rate of intoxication from Maple solving DE

a t R a t * t - exp * :

a t C a t * t - exp * t int maple :

a t C a t - exp * 1 t + (* -

a 1 :

t C a 1 t - exp 1 t + (* - (* :

t R a t * t - exp * :

Intoxication

x fnct mtp mtp,multitraceplot t 010 0.025 range : i 1 t rows range y i el t i el fnct : 11 line for t y augment 41 line :

Abs x C mtp :

Abs = Absorbed intox over time

RoC x R mtp :

RoC = actual test of intox

1 R 0.368

a e / 0.368

Abs RoC a e / 3 1 sys

Function R(a,t) is the solution of the DE [d/dt]a*(1-t)*exp(-t)

a t DE a 1 t - (* t - exp * ≡

a 1 t - (* t - exp * t int maple a t - exp * t * ≡

Explain/demonstrate the model 1g/L [one gramme/Litre].

@ time t(0) =>

a e :

t Ae a t * t - exp * :

Ae x Ae mtp :

t tol 0.5 :

@ what time [hr] tol is reached ?

Xhr a t * t - exp * t tol - t 010 solve :

minutes 1 :

hr 1 :

Xhr hr 0.23 2.68 21 mat

0.23 60 * minutes 13.8

NonSober t 0.23 2.68 0.3 range : i 1 t rows range y i el a t i el * t i el - exp * : 11 line for t y augment 31 line :

Note that 1g/L is the max of the evolution of the intoxication.

Ae x tol 2 1 sys

Plateau

Plateau 0.5 1 1.5 122 mat :

Ymarker

V 1 1.5 1022 mat :

NS NonSober 1 col NonSober 2 col o 8 black plotG :

Title 0.25 0.15 Evolution of alcoholic intoxication 12 black 15 mat :

NonSober laps time [hr] after one shot drink @ max rate 1 g/L

Ae x tol NS V Title Plateau 6 1 sys

Revisit the project

a 2.7183

t DE a 1 t - (* t - exp * :

t R a t * t - exp * :

t C a 1 t - exp 1 t + (* - (* :

-----------------------------------------

DiffEQ x DE mtp :

Peak intoxication [worst alcotest] => 1 hr i.e: ½ min DE => 2 hr

RoC x R mtp :

Abs x C mtp :

The generating DE @ init a = e

DiffEQ RoC Abs a 4 1 sys

The cumulative integral [Abs] of the rate of change [RoC] is asymptotic 2the initial DE(0)= a In this revisit, the drinker has absorbed in one shot alcohol 'a' the equivalent of a = 2.72 g/L. If the drinker is brought to hospital on his raising rate he will test much higher than tested in-situ on the road. -------------------------------- "In general, the liver can process one ounce of liquor (or one standard drink) in one hour. If you consume more than this, your system becomes saturated, and the additional alcohol will accumulate in the blood and body tissues until it can be metabolized."