Skip to content
MathsGenie logo
Open app

Course home

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

1.7 D: Sequences and series

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242
Question 138

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

The concentrations of two enzymes, Enzyme A and Enzyme B, are being monitored in a laboratory bioreactor. Initially, there are 800 units of Enzyme A.

A model predicts that the quantity of Enzyme A will increase by 6% each hour, so that the number of units of Enzyme A at the end of each hour forms a geometric sequence.

a.

Find, according to the model, the number of units of Enzyme A in the bioreactor 12 hours after monitoring began. Give your answer to 3 significant figures.

[2]
b.

The quantity of Enzyme B is being monitored over the same period. Given that:

  • 2 hours after monitoring began there were 3200 units of Enzyme B
  • 5 hours after monitoring began there were 2400 units of Enzyme B
  • the quantity of Enzyme B at the end of each hour is modelled as a geometric sequence

Find the equation of this model in the form

N=abt N = ab^t N=abt

where NNN is the number of units of Enzyme B, ttt hours after monitoring began, and aaa and bbb are constants. Give the value of aaa and the value of bbb to 2 significant figures.

[4]
c.

When t=Tt = Tt=T, the quantity of Enzyme A is equal to the quantity of Enzyme B.

Find, according to the models, the value of TTT, giving your answer to one decimal place.

[4]

1.7 D: Sequences and series Questions

  1. A Level
  2. /Maths
  3. /1.7 D: Sequences and series

Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (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.

Question bank