The efficiency E E\,E of a high-pressure industrial catalyst is modeled as a function of its concentration t t\,t by the expression E(t)=(2−1.5t)9E(t) = (2 - 1.5t)^9E(t)=(2−1.5t)9.
Find the first 4 terms, in ascending powers of ttt, of the binomial expansion of
(2−1.5t)9 (2 - 1.5t)^9 (2−1.5t)9giving each term in simplest form.
This expansion is to be used to find an approximation for the catalyst efficiency when E=1.979E = 1.97^9E=1.979. State the value of t t\,t that should be used. (There is no need to carry out this calculation.)
308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, 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). Each one has a worked solution and a mark scheme showing where the marks go.