**?? - 2016 Q9**

9. The amount of an antibiotic in the bloodstream, from a given dose, is modelled by the formula

where

A first dosage of 15mg of the antibiotic is given.

(a) Use the model to find the amount of the antibiotic in the bloodstream 4 hours after the dose is given. Give your answer in mg to 3 decimal places. (2)

A second dose of 15mg is given 5 hours after the first dose has been given. Using the same model for the second dose,

b) show that the

No more doses of the antibiotic are given. At time T hours after the second dose is given, the total amount of the antibiotic in the bloodstream is 7.5 mg

(c) Show that

*x*is the amount of the antibiotic in the bloodstream in milligrams, D is the dose given in milligrams and t is the time in hours after the antibiotic has been given.A first dosage of 15mg of the antibiotic is given.

(a) Use the model to find the amount of the antibiotic in the bloodstream 4 hours after the dose is given. Give your answer in mg to 3 decimal places. (2)

A second dose of 15mg is given 5 hours after the first dose has been given. Using the same model for the second dose,

b) show that the

**total**amount of the antibiotic in the bloodstream 2 hours after the second dose is given is 13.754 mg to 3 decimal placesNo more doses of the antibiotic are given. At time T hours after the second dose is given, the total amount of the antibiotic in the bloodstream is 7.5 mg

(c) Show that

where

*a*and*b*are integers to be determined (4)