Alcohol After a large number of drinks, a person has a blood alcohol level of 200 mg/dL (milligrams per deciliter). If the amount of alcohol in the blood decays exponentially, and after 2 hours, 112.5 mg/dL remain, find an exponential model for the person’s blood alcohol level, and use your model to estimate the person’s blood alcohol level after 4 hours. HINT [See Example 2.]
Example 2:
Find an equation of the exponential curve through (1, 6.3) and (4, 170.1).
Solution We want an equation of the form
Substituting the coordinates of the given points, we get
If we now divide the second equation by the first, we get
Now that we have b, we can substitute its value into the first equation to obtain
We have both constants, A = 2.1 and b = 3, so the model is
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