Write an equation that shows the relationship between x and y.

The equation that shows the relationship between x and y is [tex]y =2(2)^x[/tex]The table represents an exponential function.An exponential function is represented as:[tex]y = ab^x[/tex]From the table, we have the following ordered pairs(1,4) and (3,16)At (1,4), we have:[tex]ab = 4[/tex]At (3,16), we have:[tex]ab^3 = 16[/tex]Divide both equations[tex]\frac{ab^3}{ab} = \frac{16}{4}[/tex][tex]b^2 = 4[/tex]Take the square roots of both sides[tex]b =2[/tex]Recall that:[tex]ab =4[/tex]Make a the subject[tex]a = \frac 4b[/tex]So, we have:[tex]a = \frac 42[/tex][tex]a =2[/tex]Substitute values for a and b in: [tex]y = ab^x[/tex][tex]y =2(2)^x[/tex]Hence, the equation that shows the relationship between x and y is [tex]y =2(2)^x[/tex]Read more about exponential functions at: