Question

Fine the equation of the exponential function represented by the table below:

X | Y

0 | 4
1 | 16
2 | 64
3 | 256

Answer 1

`{\Large \begin{array}{llll} y = ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \textit{we know that} \begin{cases} x=0\\ y = 4 \end{cases}\implies 4=ab^0\implies 4=a(1)\implies 4=a \\ ~\hfill \underline{y=4b^2} \\\\[-0.35em] ~\dotfill\\\\ \textit{we also know that} \begin{cases} x=2\\ y = 64 \end{cases}\implies 64=4b^2\implies \cfrac{64}{4}=b^2 \\\\\\ 16=b^2\implies √(16)=b\implies 4=b~\hfill \underline{y = 4(4)^x}`