Skip to content
MathsGenie logo
Quick links
Open app

Course home

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

3.6.5 Differentiation (A-level only)

EasyMediumHard
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788899091
Question 78

The mass, MMM kg, of a block of dry ice as it sublimates in a controlled environment ttt hours after the start of an experiment is modelled by the equation

M=12+Pe−kt M = 12 + Pe^{-kt} M=12+Pe−kt

where PPP and kkk are positive constants.

Given that the mass of the block at the start of the experiment was 404040 kg,

a.

find the value of PPP.

[1]
b.

Given also that, exactly 5 hours after the start of the experiment, the mass of the block was 252525 kg,

find the value of kkk to 3 significant figures.

[3]
c.

Using the values for PPP and kkk,

find, according to the model, the rate of change of the mass of the block exactly 8 hours after the experiment started. Give your answer in kg h−1\text{kg}\text{ h}^{-1}kg h−1 to 3 significant figures.

[3]
d.

Explain why, according to the model, the mass of the block cannot fall to 101010 kg.

[1]

3.6.5 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.6.5 Differentiation (A-level only)