so, let's see 11 years ago.. let's say our years "t" is 0, or the original starting price, so t = 0, and we know the house was 100000
[tex]\bf \qquad \textit{Amount for Exponential change}\\\\
A=P(1\pm r)^t\qquad
\begin{cases}
A=\textit{accumulated amount}\to &100000\\
P=\textit{starting amount}\\
r=rate\\
t=\textit{elapsed period}\to &0\\
\end{cases}
\\\\\\
10000=P(1+r)^0\implies 10000=P\cdot 1\implies 100000=P\\\\
-------------------------------\\\\
meaning\implies \boxed{A=10000(1+r)^t}[/tex]
11 years later, t = 11, the price has appreciated to 196,000 what's the rate "r"?
[tex]\bf A=10000(1+r)^t\
\begin{cases}
A=196000\\
t=11
\end{cases}\implies 196000=100000(1+r)^{11}
\\\\\\
\cfrac{196000}{100000}=(1+r)^{11}\implies \cfrac{49}{25}=(1+r)^{11}\implies \sqrt[11]{\cfrac{49}{25}}=1+r
\\\\\\
\sqrt[11]{\cfrac{49}{25}}-1=r\implies 0.063087\approx r\qquad 0.063087\cdot 100\implies 6.3087
\\\\\\
6.3\% \approx r[/tex]
