202212061712 Solution to 1967-CE-AMATH-I-X

If the population of Hong Kong is $4$ million in $1967$ and it increases by $3\%$ each year, what will be the estimated population in $1987$ ? Give your answer correct to $4$ significant figures.

Roughwork.

$\begin{aligned} & \quad\enspace (4\times 10^6)(1+3\%)^{(1987-1967)} \\ & = (4\times 10^6)(1+0.03)^{20} \\ & = (4\times 10^6)\sum_{n=0}^{20}\begin{pmatrix}20\\ n\end{pmatrix}(1)^{20-n}(0.03)^n \\ & = (4\times 10^6)\sum_{n=0}^{20}\begin{pmatrix}20\\ n\end{pmatrix}(0.03)^n \\ & = \cdots \\ \end{aligned}$

This problem is not to be attempted.

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