A curve and two labeled points on the curve are plotted in quadrant 1 of a coordinate plane.

Question

Given the graph of the exponential equation, write the correct exponential equation for the graph.
The points are labeled as: (0,3) and (1,4.5).

(1 point)
Responses

y=3/2(3)^x
y equals Start Fraction 3 over 2 End Fraction left parenthesis 3 right parenthesis superscript x baseline

y=3(2/3)^x
y equals 3 left parenthesis Start Fraction 2 over 3 End Fraction right parenthesis superscript x baseline

y=2(3/2)^x
y equals 2 left parenthesis Start Fraction 3 over 2 End Fraction right parenthesis superscript x baseline

y=3(3/2)^x
y equals 3 left parenthesis Start Fraction 3 over 2 End Fraction right parenthesis superscript x baseline
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Answer 1

To find the exponential equation that matches the points (0, 3) and (1, 4.5), we can assume the form of the exponential equation is:

$$y=a(b^x)$$

Where:

• $a$ is the initial value at $x=0$
• $b$ is the growth factor

Step 1: Identify $a$ from the point (0, 3)

From the point (0, 3), we know:

$$y=a(b^0)⟹y=a(1)⟹a=3$$

Step 2: Substitute $a$ into the equation

Our equation now looks like:

$$y=3(b^x)$$

Step 3: Use the second point (1, 4.5) to find $b$

Using the point (1, 4.5):

$$4.5=3(b^1)⟹4.5=3b$$

Now solve for $b$:

$$b=\frac{4.5}{3}=1.5$$

Step 4: Write the final equation

Substituting $b$ back into the equation gives us:

$$y=3({1.5}^x)$$

Find the corresponding form in the options

Now we need to see which of the provided options this matches.

Recognizing that $1.5$ can be rewritten as $\frac{3}{2}$, we can express the equation as:

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

Conclusion

Comparing with the options provided, the correct answer is:

y = 3(3/2)^x

So, the correct response is:

y=3(3/2)^x