Use the image to answer the question.

Question

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

Given the graph of the exponential equation, write the correct exponential equation for the graph.

(1 point)
Responses

y=2(32)x
y equals 2 left parenthesis Start Fraction 3 over 2 End Fraction right parenthesis superscript x baseline

y=32(3)x
y equals Start Fraction 3 over 2 End Fraction left parenthesis 3 right parenthesis superscript x baseline

y=3(32)x
y equals 3 left parenthesis Start Fraction 3 over 2 End Fraction right parenthesis superscript x baseline

y=3(23)x
y equals 3 left parenthesis Start Fraction 2 over 3 End Fraction right parenthesis superscript x baseline
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Answer 1

To determine the correct exponential equation from the options given, we would typically need to analyze the graph of the curve and the labeled points to identify a proper base and scaling factor. However, since I don't have access to the image of the graph you're referring to, I can guide you on how to choose the right equation based on common characteristics of exponential functions.

Exponential equations are usually of the form:

\[ y = a(b)^x \]

Where:

• \( a \) is a constant (the initial value),
• \( b \) is the base (growth factor).

Here’s how you can evaluate the options:

1. Identify the initial value from the graph. This would be the value of \( y \) when \( x = 0 \).
2. Determine the growth factor by finding how quickly \( y \) increases as \( x \) increases. Look for points on the curve to find the multiplier rate between increasing \( x \) values.
3. Match these findings to one of the given options.

Make sure to confirm:

• Whether the graph appears to be increasing (exponential growth) or decreasing (exponential decay).
• The suggested form will directly lead you to identifying the correct coefficients and base in the listed equations.

If you can analyze the graph and provide the coordinates of the two labeled points, I can help you better determine which equation is correct based on that data.