The problem asks us to identify which of the given equations (A to E) could represent the exponential graph shown in the image. The options are: A. $y = 3(2)^x$ B. $y = 2(3)^x$ C. $y = 6(2)^x$ D. $y = 3 + 2x$ E. $y = 2 + 3x$

1. Problem Description

The problem asks us to identify which of the given equations (A to E) could represent the exponential graph shown in the image. The options are:

A. $y = 3(2)^x$

B. $y = 2(3)^x$

C. $y = 6(2)^x$

D. $y = 3 + 2x$

E. $y = 2 + 3x$

2. Solution Steps

First, observe the graph. When $x=0$, the value of $y$ appears to be approximately

3. This observation can help us eliminate some options.

Let's test each equation at $x=0$:

A. $y = 3(2)^0 = 3(1) = 3$. This could be the correct equation.

B. $y = 2(3)^0 = 2(1) = 2$. This is incorrect.

C. $y = 6(2)^0 = 6(1) = 6$. This is incorrect.

D. $y = 3 + 2(0) = 3 + 0 = 3$. This is a linear equation, so it is not exponential.

E. $y = 2 + 3(0) = 2 + 0 = 2$. This is a linear equation, so it is not exponential.

Now, let's look at $x=1$. The value of $y$ appears to be approximately

6. Let's test equation A at $x=1$:

$y = 3(2)^1 = 3(2) = 6$. This could be correct.

Let's look at $x=2$. The value of $y$ appears to be approximately

1

2. Let's test equation A at $x=2$:

$y = 3(2)^2 = 3(4) = 12$. This matches.

3. Final Answer

A. $y = 3(2)^x$