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

y=3(32)x

Answer 1

To determine the correct exponential equation for the graph, let's analyze the typical form of an exponential function. The general form is:

\[ y = a \cdot b^x \]

where \( a \) is the initial value (y-intercept when \( x = 0 \)), and \( b \) is the base of the exponential function.

Unfortunately, without the visual of the graph or points indicated on the curve, I can't ascertain the exact values of \( a \) and \( b \). However, if the points are on the graph, you can identify \( a \) and the growth or decay factor \( b \) from the plotted points (for example, see how y changes with each unit of x).

From the given options, identifying the correct equation will involve matching the observed points on the graph with the appropriate format of the exponential equations provided.

Since I'm unable to see the image, choose an equation that closely matches the behavior of the graph:

If the graph shows increases: Look for an equation with a base \( b > 1 \) (indicating growth).

If the graph shows decreases: Look for an equation with a base \( 0 < b < 1\) (indicating decay).

Please review the points plotted and how they relate to the options you provided, and you will be able to select the correct one accordingly. If you're able to share more details about the specific coordinates or values in the graph, I might be able to help further!