** ?? - 2016 Q9 ANSWERS**

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

where 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

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

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)