The temperature, TTT Kelvin, of a superconducting material being cooled in a cryogenic chamber after sss seconds is modeled by the equation:
log10T=1.94−0.12s \log_{10} T = 1.94 - 0.12s log10T=1.94−0.12sShow 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.
With reference to the equation in part (a), interpret the value of the constant aaa.
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−sUse calculus to find, to 2 significant figures, the value of dTds\frac{dT}{ds}dsdT when s=3s = 3s=3.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions 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, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
