An ecological model for the expansion of a species population defines the growth intensity, I(k)I(k)I(k), after kkk observation cycles. The value of I(k)I(k)I(k) is given by the coefficient of tkt^ktk in the binomial expansion of:
A(t)=(32+2t)11 A(t) = \left(\frac{3}{2} + 2t\right)^{11} A(t)=(23+2t)11Calculate the value of the growth intensity after 7 observation cycles, I(7)I(7)I(7), giving your answer in simplest form.
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.