Find Constants A,B, and k such that f(x)=A2^(kx)+B satisfies

[phawksbball24]

Find constants A, B, and k such that the equation f(x) = A2^(kx)+b satisfies the following three conditions:
- f(x) is always decreasing
- f(x) has a horizontal asymptote at y=1, and
- f(x) goes through the point (0, 4)

I am basically confused on where to even start but I believe it must be negative to insure that it is always decreasing, must be shifted up to have horizontal asymptote at y=1

I could be wrong with those but my biggest problem is getting the equation to go through the point (0, 4) Any help you could provide me would be greatly appreciated, thanks

 

[pka]

Here is the graph. I found the function; so can you.

 

[phawksbball24]

thanks