Skip to content
MathsGenie logo
Quick links
Open app

Course home

  1. A Level
  3. Maths CCEA
  5. Question bank

3.5.1 Differentiation (A-level only)

EasyMedium
123456789101112131415
Question 10

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]

3.5.1 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.5.1 Differentiation (A-level only)