Question 234877
the percentage of alcohol in a person's bloodstream t hr after drinking 8 fluid oz of whiskey is given by:
A(t)=.29te^-4t (0<=t<=12)
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(a) what is the percentage of alcohol in a person's bloodstream after 1/2 hour?
{{{A(1/2) = 0.29*0.5*e^-2}}}
A(1/2) = 0.1962%
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 7hrs?
{{{A(7) = 0.29*7*e^-28}}}
A(7) = 1.4036 * 10^-12
= 0.0000000000014036%
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(b) How fast is the percentage of alcohol in a person's bloodstream changing after 1/2 hr? 7 hr? 
{{{dA/dt = 0.29e^-4t*(1-4t)}}}
@1/2 {{{dA/dt = (0.29*e^-2)*(1 - 2)}}}
= -0.039%/hour
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@7 {{{dA/dt = (0.29*e^-28)*(1-28)}}}
= (-5.414E-12)%/hour
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This equation is not valid, at 7 hours the rate of change per hour is greater than the remaining concentration by a factor of ~ 4.