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3.6.5 Differentiation (A-level only)

3.6.5 Differentiation (A-level only)

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Question 70

The pressure, PPP kPa, inside a vacuum chamber ttt seconds after a suction pump is activated is modelled by the equation

P=15+Ae−kt P = 15 + Ae^{-kt} P=15+Ae−kt

where AAA and kkk are positive constants.

Given that the pressure inside the chamber at the instant the pump was activated was 100100100 kPa,

a.

find the value of AAA.

[2]
b.

Given also that, exactly 15 seconds after the pump was activated, the pressure was 404040 kPa,

find the value of kkk to 3 significant figures.

[4]
c.

Using the values for AAA and kkk,

find, according to the model, the rate of change of the pressure inside the chamber exactly 5 seconds after the pump was activated. Give your answer in kPa s−1\text{kPa}\,\text{s}^{-1}kPas−1 to 3 significant figures.

[3]
d.

Explain why, according to the model, the pressure cannot fall to 101010 kPa.

[2]
Markscheme

3.6.5 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6.5 Differentiation (A-level only)

133 exam-style questions on WJEC A Level Maths 3.6.5 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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