Question

Find an exponential function with a horizontal asymptote y equals=2 whose graph contains the points ​(0,3​) and ​(1,6​).

Answer 1

$\bf y=a(b)^x\qquad \qquad (\stackrel{x}{0}~,~\stackrel{y}{3})\implies 3=a(b)^0\implies 3=a \\\\\\ therefore\qquad y=3(b)^x\\\\ -------------------------------\\\\ (\stackrel{x}{1}~,~\stackrel{y}{6})\implies 6=3(b)^1\implies \cfrac{6}{3}=b^1\implies 2=b \\\\\\ therefore\qquad y=3(2)^x$

now, exponential functions have a horizontal asymptote at the x-axis, namely when y = 0, however, if you just move this one with a vertical translation of 2, then the horizontal asymptote will be at 2 instead.    y = 3(2)ˣ + 2