House increase percentage

On the pages of the Czech Statistical Office, we can learn that in 1869, Prague and its suburbs had a total of 10,947 houses; in 1900, there were 18,838 houses. What was the annual percentage "increase" of houses in Prague between 1869 and 1900, assuming a constant percentage "increase"?

Final Answer:

p =  1.7664 %

Step-by-step explanation:

$$\begin{gathered} a=10947 \\ b=18838 \\ t=1900-1869=31 \\ b=a\cdot q^t \\ b/a=q^t \\ q=(b/a{)}^{1/t}=\sqrt[31]{18838/10947}\doteq 1.0177 \\ q=1+p/100 \\ p=100\cdot (q-1)=100\cdot (1.0177-1)=1.7664\% \end{gathered}$$

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