The concentration C of a drug in a patient's bloodstream t hours after injection is given by

Question

COLLEGE ALGEBRA

c=15*(t/66+t^2)

How long does this drug stay in someone's bloodstream? Assume that the drug is out of the patients system once the concentration has decreased to 0.6 %? (round to two decimal places) If your solution is a complex or imaginary number, enter "NAN" for "Not a Real Number".

Answer 1

For this question about half life and concentration, they are giving you 0.6% for the concentration goal. So when this drug is less than 1% left in the system is when they consider it out of their bloodstream. So you substitute the 0.6% in for c (concentration) and solve for t (time). Time will be in hours.

So first convert 0.6% to .006 then that = 15*(t/66 + t^2)

Solving for t, multiply both sides by 66 first to get .396 = 15(t + 66t^2)

distribute the 15 to get .396 = 15t + 990t^2

subtract .396 from both sides and solve for t using quadratic formula

990t^2 + 15t - .396 =0

t = +- 1-(Sqrt (7.9696)) /132

or t= 0.01381096 or a negative number which we throw out because we're talking about time

rounding to 2 decimal places gives us t = 0.01

since it's hours you can multiply that times 60 to get 0.6 minutes

That's not a realistic answer for how long a drug would stay in the bloodstream, so I'd have to check your formula to see what's up. Drugs don't usually leave the bloodstream in less than a minute.