y = abᵗ
we know the initial amount is 6300 on 2006, that's on year 0, namely t = 0.
we also know that it became 8200 on 2010, that's 4 years later, namely t = 4.
what would its value be in 2019, well that's t = 13.
[tex]y = ab^t \\\\[-0.35em] ~\dotfill\\\\ \underset{t=0\hfill }{6300=ab^0}\implies 6300-a(1)\implies 6300=a~\hfill \underline{y=6300b^t} \\\\[-0.35em] ~\dotfill\\\\ \underset{t=4\hfill }{8200=6300b^4}\implies \cfrac{8200}{6300}=b^4\implies \cfrac{82}{63}=b^4\implies \sqrt[4]{\cfrac{82}{63}}=b \\\\\\ ~\hfill \underline{y=6300\left( \sqrt[4]{\frac{82}{63}} \right)^t} \\\\[-0.35em] ~\dotfill\\\\ \textit{when t = 13}\qquad \qquad y=6300\left( \sqrt[4]{\frac{82}{63}} \right)^{13}\implies y\approx 14838.1168[/tex]