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 OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.