Mathematics: 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.

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After alcohol is fully absorbed into the body,

nakeytrag

02.01.2022

$C(t)=(0.5)e^{-\frac{ln 2}{1.5}t}$

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 : $C(t)=C_oe^{-kt}$

Where C_0 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 : $t_{\frac{1}{2}} =\frac{ln 2}{k}$

$1.5=\frac{ln 2}{k}$

$k=\frac{ln 2}{1.5}$

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

So, C_0=0.5

So, $C(t)=(0.5)e^{-\frac{ln 2}{1.5}t}$

Hence an exponential decay model for your BAC t hours after midnight is $C(t)=(0.5)e^{-\frac{ln 2}{1.5}t}$

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