Part (a)
We know that at x = 0, y = 1.2
Since x is the exponent, then [tex]a^{0} = 1, a \neq 0[/tex]
Thus, given the form [tex]y = ab^{x}[/tex], we can find what a is.
[tex]1.2 = a(1); a = 1.2[/tex]
[tex]3.96 = 1.2b^{1}[/tex]
[tex]3.3 = b[/tex]
Thus, our equation becomes: [tex]y = 1.2 \cdot 3.3^{x}[/tex]
Part (b)
Once again, we can find what a is.
[tex]a = 5[/tex]
[tex]180 = 5b^{2}[/tex]
[tex]36 = b^{2}[/tex]
Taking the positive solution, we get: [tex]b = 6[/tex]
Thus, our equation becomes: [tex]y = 5 \cdot 6^{x}[/tex]
