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1.7 Differentiation

1.7 Differentiation

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Question 182

The mass, MMM kg, of a block of dry ice as it sublimates in a controlled environment ttt hours after the start of an experiment is modelled by the equation

M=12+Pe−kt M = 12 + Pe^{-kt} M=12+Pe−kt

where PPP and kkk are positive constants.

Given that the mass of the block at the start of the experiment was 404040 kg,

a.

find the value of PPP.

[1]
b.

Given also that, exactly 5 hours after the start of the experiment, the mass of the block was 252525 kg,

find the value of kkk to 3 significant figures.

[3]
c.

Using the values for PPP and kkk,

find, according to the model, the rate of change of the mass of the block exactly 8 hours after the experiment started. Give your answer in kg h−1\text{kg}\text{ h}^{-1}kg h−1 to 3 significant figures.

[3]
d.

Explain why, according to the model, the mass of the block cannot fall to 101010 kg.

[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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