Question

Write an exponential function in the form y=ab^x that goes through points (0,14) and (3,4802).

Answer 1

$y = ab^x \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y=14 \end{cases}\implies 14~~ = ~~ab^0\implies 14=a(1)\implies 14=a~\hfill \underline{y=14b^x} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=3\\ y=4802 \end{cases}\implies 4802~~ = ~~14b^3\implies \cfrac{4802}{14}=b^3 \\\\\\ 343=b^3\implies \sqrt[3]{343}=b\implies 7=b~\hfill \underline{y=14(7)^x}$