The given graph represents the function $y = C \cdot a^x$, and the task is to determine the values of $C$ and $a$. To proceed:

1. Find $C$:
   In an exponential function of the form $y = C \cdot a^x$, the value of $C$ corresponds to the $y$-intercept (the point where $x = 0$). Check the graph at $x = 0$ and note the $y$-coordinate.

2. Find $a$:
   To determine $a$, pick another point from the graph, substitute it into the equation $y = C \cdot a^x$, and solve for $a$. Commonly, the values of $y$ at integer values of $x$ are used.

I’ll zoom in on the details from the uploaded image:

• The graph passes through two visible points of interest:
  • $(0, 2)$, which gives $C = 2$.
  • Another clear point, for example $(1, 4)$, which can help solve for $a$. Substituting into $y = 2 \cdot a^x$, we have:
    $4 = 2 \cdot a^1 \implies a = 2.$

Thus, the equation is: $y = 2 \cdot 2^x$

Would you like further clarification or verification for other points?

Related Questions:

1. How does the value of $C$ affect the shape of an exponential graph?
2. What happens if $a > 1$ versus $0 < a < 1$ in $y = C \cdot a^x$?
3. How would the graph look if $C$ were negative?
4. Can $a$ be negative in $y = C \cdot a^x$? Why or why not?
5. How can exponential functions be used in real-world applications?

Tip:

For exponential equations, always check the $y$-intercept first—it simplifies determining $C$ immediately.