Question

**Show all work and label answers for full credit. Box in your final answers." 1. When a person takes an ibuprofen pill, the amount of ibuprofen (in milligrams) in the person's bloodstream can be modeled by the function P(t) = 400(0.71)' where t represents the time in hours after the pill is taken. a. How much ibuprofen is taken initially? (2 pts.) 400 b. According to this model, is the amount of ibuprofen increasing or decreasing over time? (2 pts.) decreasing Glve the percent change in the amount of ibuprofen in the bloodstream each hour. c. According to this model, what should the concentration ibuprofen be two hours after the medicine taken? Round to two decimal places. (2 pts.) d. Suppose an individual needs a second dose of ibuprofen when the level of medicine in the bloodstream reaches 18 mg. According to the model and using algebra, determine the number of hours before the second pill should be administered. Round to 2 decimal places. (5 pts.) 137

Answer 1

Amount of ibuprofen pill in the person's blood- strem is modeled by Plt) = 400/0.72) + (a) Amount of ibuprofen initially ie at tao. so Plo)= 400 (0.710° stri = 400 so Amount of ibuprofen initially is 400 mg (6) Amount of ibuprofen ý decuasing as Ni 10.74 + is decreasing function. As ar is increasing if as I I an is decreasing ifocall increasing if an of ibuprofen in percent change in amount bloodstream each hour P(x+1)-Plt) x 100 Plt)

where Plt) is amount of ibuprofen Pltl) is amount of ibuprofen at at time te time littl) tt) percentage change - 400 (0.71) _400(0.7) 400 (0.71) et 100 2 -1} & X 10ο 400 (0.71) + [ 0.71 400 (0.71) + = -29% so decrease. after (c) concentration medicine is take of ibuprofen two hours is P(2) = 400 (0.717² Pla) = 201.64

(d) of so No. of hours before and Pill is taken. = ? As and pill is taken when ibuprofen level medicine in blood stream reaches 18 ng and pill is taken when Plt)= 18 400 (0.71 t = 18 (0.71)* = 10 0 = 0.045 t log 10.71) = log (0.045) t= log (0.045) = 9.05 Log (0.71) [t=905] after 9.05 hours and pill shoul be administered. So