SOLUTION: 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) (a) what is the percentage of alcohol in a

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 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) (a) what is the percentage of alcohol in a      Log On


   

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)
(a) what is the percentage of alcohol in a person's bloodstream after 1/2 hour? 7hrs?
(b) How fast is the percentage of alcohol in a person's bloodstream changing after 1/2 hr? 7 hr?

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
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%281%2F2%29+=+0.29%2A0.5%2Ae%5E-2
A(1/2) = 0.1962%
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7hrs?
A%287%29+=+0.29%2A7%2Ae%5E-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%2Fdt+=+0.29e%5E-4t%2A%281-4t%29
@1/2 dA%2Fdt+=+%280.29%2Ae%5E-2%29%2A%281+-+2%29
= -0.039%/hour
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@7 dA%2Fdt+=+%280.29%2Ae%5E-28%29%2A%281-28%29
= (-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.