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 - 0.12slog10T=1.94−0.12s
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.
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−sT = 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.
Practise Edexcel A Level Maths 9.2 Differentiating exponentials and logarithms with exam-style questions for A Level Maths. 23 questions, 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.