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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
