The signal noise N N\,N in a high-precision sensor is modeled by the function N(c)=(3+c4)9\displaystyle N(c) = \left(3 + \frac{c}{4}\right)^9N(c)=(3+4c)9, where c c\,c represents the concentration of a dopant in parts per million (ppm).
Find, in ascending powers of ccc, up to and including the term in c3c^3c3, the binomial expansion of N(c)N(c)N(c), fully simplifying each coefficient.
Use your expansion from part (a) to find an approximation for 3.02593.025^93.0259. Give your answer to 2 decimal places.
Without calculating the exact value of 3.02593.025^93.0259, state, with a reason, whether the answer to part (b) is an underestimate or an overestimate.
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.
