Question

Write an exponential function in the form y=ab^x that goes through points (0, 14) and (6, 896)

Answer 1

$y = ab^x \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y=14 \end{cases}\implies 14~~ = ~~ab^0\implies 14=a(1)\implies 14=a~\hfill \underline{y=14b^x} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=6\\ y=896 \end{cases}\implies 896~~ = ~~14b^6\implies \cfrac{896}{14}=b^6 \\\\\\ 64=b^6\implies \sqrt[6]{64}=b\implies 2=b~\hfill \underline{y=14(2)^x}$