the general form of the exponential function is
[tex]y=a^x+b[/tex]first replace (0,20)
[tex]\begin{gathered} 20=a^0+b \\ 20=1+b \\ b=20-1=19 \end{gathered}[/tex]for now, the formula is
[tex]y=a^x+19[/tex]now, replace (3,1280)
[tex]\begin{gathered} y=a^x+19 \\ 1280=a^3+19 \\ a^3=1280-19 \\ a^3=1261 \end{gathered}[/tex][tex]a=\sqrt[3]{1261}=10.8[/tex]so, the exponential function is
[tex]y=10.8^x+19[/tex]