help with half-life question

Question

A 10 mg dose of the drug Oxycodone has a 1/2 life of about 5 hours. Let S(t) be the amount of drug in mg in a patients body as a function of time, t hours after taking the drug.

 

a. write an equation to model the decay of the drug as a function of time.

Answer 1

Decay problems are exponential.  Half-life means that after 5 hours you will have half of the amount of the drug left than you started with,  Since that is at time t=5, you first need to calculate the decay constant using natural logs.  Then you can use that to write the equation.