Question

Write an exponential function in the form y=ab^x that goes through points (0,4) and (5, 128)

Answer 1

`y=ab^x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know that}}{(\stackrel{x}{0}~~,~~\stackrel{y}{4})}\implies 4=ab^0\implies 4=a(1)\implies 4=a~\hfill \underline{y=4b^x} \\\\\\ \stackrel{\textit{we also know that}}{(\stackrel{x}{5}~~,~~\stackrel{y}{128})}\implies 128=4b^5\implies \cfrac{128}{4}=b^5\implies 32=b^5 \\\\\\ \sqrt[5]{32}=b\implies 2=b~\hfill \underline{y=4(2)^x}`