Question

Write an exponential function in the form y=ab^x that goes through points (0, 18) and (9,9216).

Answer 1

`y=ab^x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know that}}{x=0\qquad y=18}\qquad 18=ab^0\implies 18=a(1)\implies 18=a~\hfill \underline{y=18b^x} \\\\\\ \stackrel{\textit{we also know that}}{x=9\qquad y=9216}\qquad 9216=18b^9\implies \cfrac{9216}{18}=b^9 \\\\\\ 512=b^9\implies \sqrt[9]{512}=b\implies 2=b~\hfill \underline{y=18(2)^x}`