Chapter 1.5, Problem 47E

LIFE SCIENCE APPLICATIONS

Alcohol Concentration The polynomial function

$A\left(t\right)=0.003631t^3-0\cdot 03746t^2+0\cdot 1012t+0\cdot 009$

gives the approximate blood alcohol concentration in a $170-\text{lb}$ woman $t\text{hours}$ after drinking $2\text{oz}$ of alcohol on an empty stomach, for $t$ in the interval $\left[0,5\right]$. Source: Medical Aspects of Alcohol Determination in Biological Specimens.

a. Graph $A\left(t\right)$ on $0\le t\le 5$.

b. Using the graph from part a, estimate the time of maximum alcohol concentration.

c. In many states, a person is legally drunk if the blood alcohol concentration exceeds $0.08\%$. Use the graph from part a to estimate the period in which this $170-\text{lb}$ woman is legally drunk.