Question

Complete the equation for g(x)

Answer 1

`g(x)=a\cdot b^x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know that}}{(\stackrel{x}{0}~~,~~\stackrel{g(x)}{12})}\implies 12=a\cdot b^0\implies 12=a\cdot 1\implies 12=a~\hfill \underline{g(x)=12b^x} \\\\\\ \stackrel{\textit{we also know that}}{(\stackrel{x}{1}~~,~~\stackrel{g(x)}{9})}\implies 9=12b^1\implies \cfrac{9}{12}=b\implies \cfrac{3}{4}=b~\hfill \underline{g(x)=12\left( (3)/(4) \right)^x}`