ind an exponential function whose graph has the horizontal asymptote $y=-2$ and the points $(0,-1)$ and $(1,8)$.

Step 1 ：Given the horizontal asymptote $y=-2$ and the points $(0,-1)$ and $(1,8)$, we need to find an exponential function that fits these conditions.

Step 2 ：An exponential function has the form $y=a \cdot b^x + k$, where $a$ is the initial value, $b$ is the growth factor, $x$ is the variable, and $k$ is the vertical shift (which corresponds to the horizontal asymptote).

Step 3 ：Since the horizontal asymptote is $y=-2$, we know that $k=-2$.

Step 4 ：Substituting the point $(0,-1)$ into the equation gives $-1=a \cdot b^0 - 2$, which simplifies to $-1=a-2$. Solving for $a$ gives $a=1$.

Step 5 ：Substituting the point $(1,8)$ into the equation gives $8=1 \cdot b^1 - 2$, which simplifies to $8=b-2$. Solving for $b$ gives $b=10$.

Step 6 ：So, the exponential function is $y=1 \cdot 10^x - 2$, which simplifies to $y=10^x - 2$.

Step 7 ：\(\boxed{y=10^x - 2}\) is the final answer.