Population

The town has 65,000 inhabitants. 40 years ago there were 157,000. How many people will live in town in 10 years if the average rate in population is as in previous years?

Result

x =  52139

Solution:

n1=n2⋅q40 ln⁡n1=ln⁡n2+40⋅ln⁡q  ln⁡q=ln⁡65−ln⁡15740  ln⁡q=−0.022046463386317 q=e−0.022046463386317=0.97819478375318 p=−2.18 %  x=65000⋅q10=65000⋅0.9781947837531810 x=52139n_1 = n_2 \cdot q^{ 40} \ \\ \ln n_1 = \ln n_2 + 40 \cdot \ln q \ \\ \ \\ \ln q = \dfrac{ \ln 65 - \ln 157 }{ 40 } \ \\ \ \\ \ln q = -0.022046463386317 \ \\ q = e^{ -0.022046463386317} = 0.97819478375318 \ \\ p = -2.18 \ \% \ \\ \ \\ x = 65 000 \cdot q^{ 10} = 65 000 \cdot 0.97819478375318^{ 10} \ \\ x = 52139

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