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)11A(t) = \left(\frac{3}{2} + 2t\right)^{11}A(t)=(23+2t)11
Calculate the value of the growth intensity after 7 observation cycles, I(7)I(7)I(7), giving your answer in simplest form.
Practise Edexcel A Level Maths 4.2 Expanding (a + bx)^n with exam-style questions for A Level Maths. 99 questions, 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.