To determine which equation matches the graph, we analyze the given graph and the provided equations. Here's how:

Observations from the Graph:

1. Behavior of the Graph:

   • The graph shows exponential growth, as it rapidly increases for positive $x$-values and approaches 0 for negative $x$-values.

2. Key Point(s):

   • The graph passes through $(0, 10)$. This indicates that the initial value (or the coefficient $a$) is $10$, since $y = a \cdot b^x$ and at $x = 0$, $y = a$.

3. Base of the Exponential Function:

   • The growth rate implies a base greater than 1, and the only base provided in the options is $4$. Thus, the function must take the form $y = 10(4^x)$.

Answer:

The correct equation is: $\boxed{y = 10(4^x)}$

Would you like to explore further or need help plotting exponential functions?
Here are 5 related questions to expand your understanding:

1. How does the initial value $a$ affect the graph of an exponential function?
2. What does the base $b$ in $y = a \cdot b^x$ represent, and how does it change the graph?
3. What happens to the graph if $a$ is negative?
4. How can you determine the equation of an exponential function from a graph with two points?
5. What does the horizontal asymptote represent in an exponential graph?

Tip: For $x = 0$, the $y$-intercept gives the value of $a$, making it a quick way to identify the initial coefficient of an exponential function.