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1.7 Differentiation

1.7 Differentiation

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Question 191

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=m0​e−kt

where 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.

a.

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.

[4]
b.

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.

[4]
c.

State one reason why the mass of medication predicted by this model might not be accurate for an individual patient.

[1]
Markscheme

1.7 Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.7 Differentiation

425 exam-style questions on OCR A Level Maths 1.7 Differentiation, covering 1.7.1 Derivative as gradient of the tangent, 1.7.2 Gradient of the tangent at a point, 1.7.3 Sketching the gradient function, 1.7.4 Second derivatives, 1.7.5 Second derivative as rate of change of gradient, 1.7.6 Convex, concave and points of inflection (A-level only), 1.7.7 Differentiation from first principles for powers of x, 1.7.8 Differentiation from first principles for sin x and cos x (A-level only), 1.7.9 Differentiating x^n, 1.7.10 Differentiating e^(kx) and a^(kx) (A-level only), 1.7.11 Differentiating trigonometric functions (A-level only), 1.7.12 Derivative of ln x (A-level only), 1.7.13 Tangents and normals, 1.7.14 Stationary points, 1.7.15 Increasing and decreasing functions, 1.7.16 Points of inflection (A-level only), 1.7.17 Product and quotient rules (A-level only), 1.7.18 Chain rule (A-level only), 1.7.19 Parametric and implicit differentiation (A-level only), 1.7.20 Constructing differential equations (A-level only), and 1.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.

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