Answer:
[tex]\sf y = 11(3)^x[/tex]
given points: ( 0, 11) , (2,99)
solve for 1st
[tex]\sf y = ab^x[/tex]
[tex]\sf 11 = ab^0[/tex]
since we know [tex]\sf b^0 = 1[/tex]
[tex]\sf 11 =a[/tex]
solve for 2nd
[tex]\sf y = ab^x[/tex]
[tex]\sf 99 = ab^2[/tex]
[tex]\sf \dfrac{99}{b^2} = a[/tex]
solve simultaneously:
[tex]\sf 11 = \sf \dfrac{99}{b^2}[/tex]
[tex]\sf 11 b^2= \sf 99}[/tex]
[tex]\sf b^2= 9[/tex]
[tex]\sf b = 3[/tex]
Therefore equation: [tex]\sf y = 11(3)^x[/tex]
