Answer
$y=0.5^x-3$
Work Step by Step
The general formula for an exponential function can be defined as:
$y=Ca^x+b=y~~~(1)$
Where we have the horizontal asymptote $b=-3$.
In our case, equation (1) becomes:
$y=Ca^x+2=y~~~(2)$
Plug in $x=0$ and $y=-2$ to compute the values of $C$ and $a$.
$C a^0-3=-2 \\(C)(1)-3=-2\\C=1 $
Thus, equation (2) becomes: $y=a^x-3$
Now, plug in $x=-2$ and $y=1$ to compute the values of $C$ and $a$.
$y=a^x -3\\ 1=a^{-2}-3\\
1+3=\dfrac{1}{a^2} \\a^2=\dfrac{1}{4}\\
a= \pm \dfrac{1}{2}$
Thus, the required equation is $y=0.5^x-3$ because $a$ cannot be negative, so we only consider the positive value of $a$, which is $a=\dfrac{1}{2}=0.5$
