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Use the image to answer the 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=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=2(32)x
y equals 2 left parenthesis Start Fraction 3 over 2 End Fraction right parenthesis superscript x baseline

y=3(23)x

1 answer

To determine the correct exponential equation given the graph and labeled points, it would be essential to examine the specific coordinates of those points and the way the curve behaves, particularly its base and growth factor.

Since I can't see the image you mentioned, I will offer a general approach to identify the exponential equation:

  1. Find the growth factor (base): Look at how y changes as x increases. If it doubles, triples, etc., you will identify the base of the exponential function.

  2. Identify the initial value: Check the value of y when x = 0, which gives you the initial value or y-intercept.

  3. Put it all together: The exponential equation generally takes the form \( y = a(b)^x \), where \( a \) is the initial value and \( b \) is the growth factor.

Given the options:

  • \( y = 32(3)^x \)
  • \( y = \frac{3}{2}(3)^x \)
  • \( y = 3(32)^x \)
  • \( y = 2(32)^x \)
  • \( y = 3(23)^x \)

Once you identify the base and initial value from the graph, you can match the equation with the correct option. Look for indicators of growth in the points on the curve to finalize your choice.

If you can provide more detail about the points or characteristics of the curve, I can assist you further in selecting the right exponential equation.