Answer:
[tex]f(x)= 3({2})^{x} - 3[/tex]
Step-by-step explanation:
Let the equation be of the form
[tex]f(x)= a {b}^{x} + k[/tex]
be the equation, where k=-3 is the horizontal asymptote.
The equation now becomes:
[tex]f(x)= a {b}^{x} - 3[/tex]The curve passes through (0,0)
[tex]0= a {b}^{0} - 3[/tex]
[tex]0 = a - 3[/tex]
a=3
This implies that:
[tex]f(x)= 3{b}^{x} - 3[/tex]
We again substitute (1,3)
[tex]3=3{b}^{1} - 3[/tex]
[tex]3b = 6[/tex]
[tex]b = 2[/tex]
The required equation is
[tex]f(x)= 3({2})^{x} - 3[/tex]
