?? - 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 total amount of the antibiotic in the bloodstream 2 hours after the second dose is given is 13.754 mg to 3 decimal places
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 places
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
where a and b are integers to be determined (4)
ANSWERS
