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)7
Given 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 Edexcel A Level Maths Binomial Expansion with exam-style questions for A Level Maths. 100 questions covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions, matched to the Edexcel A Level Maths (9MA0) 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.