A pharmacist is studying the elimination of a medication from the bloodstream. The mass of the medication in the body is modeled by the equation
m=m0e−kt m = m_0 e^{-kt} m=m0e−ktwhere m0m_0m0 mg is the initial mass administered and mmm mg is the mass in the body after ttt hours.
On average, the biological half-life of this medication is 4.5 hours.
A patient is given a single dose of 300 mg of the medication.
The patient takes the 300 mg dose at 9 am. Use the model to estimate the mass of the medication remaining in the body at 3 pm.
The patient is instructed to ensure that the total mass of the medication in their body does not exceed 350 mg. The patient intends to take a second 300 mg dose. Using the model, find the earliest time they can take this second dose. Give your answer to the nearest minute.
State one reason why the mass of medication predicted by this model might not be accurate for an individual patient.
480 exam-style questions on AQA A Level Maths 1.11 H: Integration, covering 1.11.1 Fundamental Theorem of Calculus, 1.11.2 Integrating standard functions, 1.11.3 Definite integrals and areas, 1.11.4 Integration as the limit of a sum (A-level only), 1.11.5 Integration by substitution and by parts (A-level only), 1.11.6 Integration using partial fractions (A-level only), 1.11.7 Differential equations with separable variables (A-level only), and 1.11.8 Interpreting solutions of differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.