The power output $P$, in kilowatts, of a prototype wind turbine is modeled by the function $P(v) = \left(2 + \frac{v}{10}\right)^{12}$ 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 $0.5$ m/s, which corresponds to evaluating $2.05^{12}$. Give your answer to 2 decimal places.

Without calculating the exact value of $2.05^{12}$, state, with a reason, whether the answer to part (b) is an overestimate or an underestimate.