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.
408 exam-style questions on Edexcel A Level Maths Binomial Expansion, covering 4.1 Expanding (1 + x)^n, 4.2 Expanding (a + bx)^n, and 4.3 Using Partial Fractions. Each one has a worked solution and a mark scheme showing where the marks go.