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Differentiation

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Question 401

The temperature, TTT Kelvin, of a superconducting material being cooled in a cryogenic chamber after sss seconds is modeled by the equation:

log⁡10T=1.94−0.12s \log_{10} T = 1.94 - 0.12s log10​T=1.94−0.12s
a.

Show that this equation can be written in the form T=ab−sT = ab^{-s}T=ab−s, where aaa and bbb are constants. Give the value of aaa to the nearest whole number and the value of bbb to 2 significant figures.

[3]
b.

With reference to the equation in part (a), interpret the value of the constant aaa.

[1]
c.

When the cooling system is adjusted to a different cycle, the temperature TTT after sss seconds satisfies the equation:

T=180×1.15−s T = 180 \times 1.15^{-s} T=180×1.15−s

Use calculus to find, to 2 significant figures, the value of dTds\frac{dT}{ds}dsdT​ when s=3s = 3s=3.

[4]
Markscheme

Differentiation Questions

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

649 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.

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