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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=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
y equals 3 left parenthesis Start Fraction 3 over 2 End Fraction right parenthesis superscript x baseline
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1 answer

To determine which exponential equation matches the graph you are referring to, we need to consider the general form of an exponential function, which is typically expressed as:

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

Where:

  • \( a \) is the initial value (the y-intercept when \( x = 0 \)),
  • \( b \) is the base of the exponential function, which indicates the growth or decay rate.

From the descriptions of the options given, it looks like they involve different values for \( a \) and \( b \).

When looking at the potential answers:

  1. \( y = 2(3/2)^x \)
  2. \( y = 32(3)^x \)
  3. \( y = 3(2/3)^x \)
  4. \( y = 3(3/2)^x \)

Without the specific details of the graph, I can’t definitively tell you which one is correct, but you can analyze the graph to determine:

  • The value at \( x = 0 \) gives a clue towards \( a \).
  • The way the curve behaves (increasing or decreasing) will help you identify \( b \).

Please examine the graph for these characteristics to select the correct exponential equation. If you have specific values or details from the graph, feel free to share them, and I can help further analyze the options!