Certainly! Here's a similar problem based on the provided one:

Problem:

Consider the function $g(x) = m(0.3)^x + n$, where $m$ and $n$ are constants. The graph of $g(x)$ passes through the points $(0, 8)$ and $(2, 4.5)$.

(a) Write down two equations relating $m$ and $n$.
(b) Solve for the values of $m$ and $n$.
(c) Write down the equation of the horizontal asymptote of the graph of $g(x)$.

Let me know if you'd like further modifications, a solution, or more related problems! 😊

Follow-up Questions

1. What type of graph does this function represent, and why?
2. How does the base of the exponential function affect the graph's shape?
3. What happens to the graph if the horizontal asymptote is shifted upward by 3 units?
4. Can $g(x) = 0$ have a real solution in this context? Why or why not?
5. How do the values of $m$ and $n$ affect the steepness and position of the graph?

Tip:

Always analyze the horizontal asymptote of an exponential function to understand its long-term behavior.