Population

The town has 55,000 inhabitants. 25 years ago, there were 85,000. If the population's average rate is the same as in previous years, how many people will live in a city in 10 years?

Final Answer:

n₃ =  46210

Step-by-step explanation:

$$\begin{gathered} n_1=55000 \\ {n}_2=85000 \\ {n}_1=n_2\cdot q^{25} \\ \ln n_1=\ln n_2+25\cdot \ln q \\ Q=\frac{\ln (n_1)-\ln (n_2)}{25}=\frac{\ln 55000-\ln 85000}{25}\doteq -0.0174 \\ Q=\ln q \\ q=e^Q=e^{(-0.0174)}\doteq 0.9827 \\ {n}_3=n_1\cdot q^{10}=55000\cdot 0.9827^{10}=46210 \end{gathered}$$

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