find exponential decay model for half life of alcohol after the body absorbs it

Question

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. 

C(t) =  

 

 

 

 

(b) Graph your BAC and use the graph to determine when you can drive home if the legal limit is 0.08 mg/mL. (A graphing calculator is recommended. Round your answer to one decimal place.) 
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