A patient has a theophylline serum concentration of 96ng/L after taking theophylline tablet. Given that the half-life of theophylline is 8hr, how long will it take for the serum concentration to reach 50mg/L (assuming the distribution is complete and that the elimination is a first order process)

Question

Thx!!!!

Answer 1

96 * (1/2)^(t/8) = 50
t = -8 ln(50/96)/ln2 = 7.53 hr

I assume that 96 and 50 are both either ng/L or mg/L

7.53 hr makes sense, since after 8 hrs the amount will be 1/2 * 96 = 48 mg/L

Answer 2

Thank you so much!!
But I want to know the equation is what??