Question

Given the graph of the exponential equation, write the correct exponential equation for the graph. (The first point is at (0, 3), The second point is at (1, 4.5).

y = 3/2(3)^x
y = 2(3/2)^x
y = 3(3/2)^x
y = 3(2/3)^x

Answer 1

To determine the correct exponential equation for the graph based on the given points, we can use the information provided.

1. **Identify the initial point (0, 3):**
- This point indicates that when \( x = 0 \), \( y = 3 \). In an exponential equation in the form \( y = ab^x \), the \( y \)-intercept \( a \) will be \( 3 \). So, we have:

\[
y = 3b^x
\]

2. **Use the second point (1, 4.5):**
- We can substitute this point into the equation. We know that when \( x = 1 \), \( y = 4.5 \):

\[
4.5 = 3b^1
\]

- To find \( b \):

\[
4.5 = 3b \implies b = \frac{4.5}{3} = 1.5
\]

- The equation now looks like:

\[
y = 3(1.5)^x
\]

- Notice that \( 1.5 \) can also be expressed as \( \frac{3}{2} \):

\[
y = 3\left( \frac{3}{2} \right)^x
\]

3. **Conclusion:**
The equation that matches the points given in the problem is:

\[
y = 3\left( \frac{3}{2} \right)^x
\]

So, the correct option from the choices provided is:

\[
y = 3\left( \frac{3}{2} \right)^x
\]