For the following exercises, find a formula for an exponential function that passes through the two points given. (0,6) and (3,750)

[tex]\boxed{\boxed{f(x)=6(5)^x}}[/tex]Explanation:An exponential function is given by the following form:[tex]y=ab^x \\ \\ Where: \\ \\ a \ is \ a \ constant \ and \ b \ is \ the \ base[/tex]Here we know two points:[tex](0,6) \ and \ (3,750)[/tex][tex]\bullet \ (0,6) \\ \\ x=0, \ y=6 \\ \\ 6=ab^0 \\ \\ \boxed{a=6} \\ \\\ \\ \bullet \ (3,750) \\ \\ x=3, \ y=750 \\ \\ 750=6b^3 \\ \\ b^3=\frac{750}{6} \\ \\ b=\sqrt[3]{125} \\ \\ \boxed{b=5}[/tex]Finally, our exponential function is:[tex]\boxed{\boxed{f(x)=6(5)^x}}[/tex]Learn more:Behavior of functions: