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

beanburito

step-by-step explanation:

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.