Exponential decrease

Question

A medicine is given with a dosage of 30mg, during the first 4 hours 17.7 mg of the drug is broken down. A body generally does this exponentially.

 

What is the rate of decay? When writing it as a formula: M(t) = 30 · ? ^t

 

With t= 0 at 30 mg

 

 

Thank you for taking the time to help.

Answer 1

y = a(1-r)^x where a = the initial value, r = decay rate, x = # of time intervals

 

Substitute: 17.7 = 30(1 - r)^1  (one time interval of 4 hours has passed)

 

Solve: 17.7 = 30 - 30r

          -13.3 = -30 r

          r = .44