The power output PPP, in kilowatts, of a prototype wind turbine is modeled by the function \
P(v) = \left(2 + \frac{v}{10}\right)^{12}{\char"24}$ where $v \ge 0$ is the wind speed in m/s. Find, in ascending powers of $v$, up to and including the term in $v^3$, the binomial expansion of $P(v)$, fully simplifying each coefficient.Use the answer to part (a) to find an approximation for the power output when the wind speed is 0.50.50.5 m/s, which corresponds to evaluating 2.05122.05^{12}2.0512. Give your answer to 2 decimal places.
Without calculating the exact value of 2.05122.05^{12}2.0512, state, with a reason, whether the answer to part (b) is an overestimate or an underestimate.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions 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), matched to the AQA A Level Maths (7357) 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.
