In a biological study, the population density P P\,P of a specific bacterial colony is modeled by the function P(c)=(4+kc)7P(c) = (4 + kc)^7P(c)=(4+kc)7, where c c\,c represents the concentration of a growth medium and k k\,k is a positive constant.
Find the first three terms, in ascending powers of ccc, in the expansion of
(4+kc)7 (4 + kc)^7 (4+kc)7Given that the coefficient of c2 c^2\,c2 in this expansion is exactly half the coefficient of ccc, determine the value of the constant kkk.
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.
