After alcohol is fully absorbed into the body, it is metabolized with a half-life of about 1.5 hours. suppose you have had three alcoholic drinks and an hour later, at midnight, your blood alcohol concentration (bac) is 0.5 mg/ml. (a) find an exponential decay model for your bac t hours after midnight.

Step-by-step explanation:

Given :

After alcohol is fully absorbed into the body, it is metabolized with a half-life of about 1.5 hours.

Your blood alcohol concentration (BAC) is 0.5 mg/mL.

To Find : Find an exponential decay model for your BAC t hours after midnight.

Solution:

General form of decay model :

Where is the initial BAC

C(t) is the BAC after t hours

k is the decay constant

Now we are given that After alcohol is fully absorbed into the body, it is metabolized with a half-life of about 1.5 hours.

Formula :

Your blood alcohol concentration (BAC) is 0.5 mg/mL..

So,

So,  

Hence an exponential decay model for your BAC t hours after midnight is

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