Question

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, 162 mg/dL remain, find an exponential model for the person's blood alcohol level f(t) where t is the time in hours. HINT [See Example 2.]

f(t) =

Use your model to estimate the person's blood alcohol level after 4 hours. (Round your answer to one decimal place.)

mg/dL

Answer 1

Let the exponential decay model will be given as

Now, since initially the level is 200 mg/dL, so we can write

Now, after 2 hours, which implies (t=2), the value of f(t) becomes 162, so we can write

Hence the person's blood alcohol level after 4 hours

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