The equation of the graph shown corresponds to one of the given options. Analyzing the shape and exponential growth, the graph suggests it represents a function of the form:

$y = a \cdot b^x$

From the visual characteristics:

1. The graph passes through points that indicate the base $b > 1$, showing exponential growth.

2. The exact coordinates of the points on the graph can be estimated or calculated. Using one of these points (for example, $x = 0$, $y = 2$):

   • When $x = 0$, $y = a$, indicating the initial value (coefficient $a$) of the function.
   • The coefficient $a$ is the y-intercept, which appears to be 2.

Testing the provided options:

• The base $b$ seems to be 3 based on the steepness of growth.
• The equation $y = 2(3^x)$ fits the given graph.

Correct Equation:

$y = 2(3^x)$

Let me know if you'd like more detailed calculations or explanations!

Related Questions:

1. What is the general form of an exponential function, and how do you identify it from a graph?
2. How can we determine the base $b$ of an exponential function by observing its growth?
3. What role does the coefficient $a$ play in the graph of an exponential function?
4. How can we verify the equation of a graph using a specific point?
5. What are some real-life examples of exponential growth functions?

Tip:

When identifying the equation of an exponential graph, always check the y-intercept and one additional point to confirm both the base $b$ and the coefficient $a$.