Question

Given the graph of the exponential equation, write the correct exponential equation for the graph.
(0,3) and (1,4.5)
(1 point)
Responses

y=3(2/3)x

y=3(3/2)x

y=3/2(3)x

y=2(3/2)x

Answer 1

To find the correct exponential equation based on the given points (0,3) and (1,4.5), we can use the general form of an exponential function, which is:

\[
y = ab^x
\]

Where:
- \(a\) is the initial value (the value of \(y\) when \(x = 0\)),
- \(b\) is the growth factor.

From the point (0,3), we can determine that:

\[
a = 3
\]

Thus, our equation becomes:

\[
y = 3b^x
\]

Now we can use the point (1,4.5) to find \(b\):

\[
4.5 = 3b^1 \implies 4.5 = 3b \implies b = \frac{4.5}{3} = 1.5 = \frac{3}{2}
\]

Now, substituting \(b\) back into our equation gives:

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

Thus, the final equation is:

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

So, the correct response is:

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