Question

What’s the exponential function of g?X 0,1,2,3,4 g(x) 1,3,9,27,81

Answer 1

In order to find the exponential function g(x), let's use the model below for an exponential function:

`g(x)=a\cdot b^x`

Using the points (0, 1) and (1, 3), we have:

`\begin{gathered} (0,1)\colon \\ 1=a\cdot b^0 \\ a=1 \\ \\ (1,3)\colon \\ 3=1\cdot b^1 \\ b=3 \end{gathered}`

Therefore the equation is g(x) = 3^x.