Skip to content

Course home

Integration

Integration

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511512513514515516517518519520521522523524525526527528529530531532533534535536537538539540541542543544545546547548549550551552553554555556557558559560561562563564565566567568569570571572573574575576577578579580581582583584585586587588589590591592593594595596597598599600601602603604605606607608609610611612613614615616617618619620621622623624625626627628629630631632633634635636637638639640641642643644645646647648649650651652653654655656657658659660661662663664665666667668669670671672673674675676677678679680681682683684685686687688689690691692693694695696697698699700701702703704705706707708709710711712713714715716717718719720721722723724725726727
Question 579

An environmental scientist is tracking the mass of substances in a filtration tank.

The mass, MMM, in milligrams, of a purifying bacteria culture is modelled by the equation

M=Aekt,t≥0 M = A e^{kt}, \quad t \ge 0 M=Aekt,t≥0

where A A\,A and k k\,k are positive constants and t t\,t is the time in hours since the bacteria were introduced.

Given that:

  • the initial mass of the bacteria was 250 mg
  • after 8 hours, the mass had increased to 1500 mg
a.

Find the exact value of A A\,A and the value of k k\,k correct to 4 significant figures.

[4]
b.

The mass, MMM, of a specific contaminant in the tank is modelled by the equation

M=12000e−0.15t,t≥0 M = 12000 e^{-0.15t}, \quad t \ge 0 M=12000e−0.15t,t≥0

where t t\,t is the time in hours since the start of the filtration process.

Find the rate of decrease of the mass of the contaminant exactly 5 hours after the start. Give your answer in mg per hour to 3 significant figures.

[3]
c.

At time t=Tt = Tt=T, the mass of the bacteria culture is equal to the mass of the contaminant.

Find the value of TTT, giving your answer to 3 significant figures.

(Solutions relying entirely on calculator technology are not acceptable.)

[4]
Markscheme

Integration Questions

  1. A Level
  2. /Maths
  3. /Integration

864 exam-style questions on Edexcel A Level Maths Integration, covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank