<math xmlns="http://www.w3.org/1998/Math/MathML" title="" display="inline">
  <semantics>
    <mstyle>
      <mi>f</mi>
      <mo>(</mo>
      <mi>x</mi>
      <mo>)</mo>
      <mo>=</mo>
      <mn>3</mn>
      <msup>
        <mfenced>
          <mfrac>
            <mn>2</mn>
            <mn>3</mn>
          </mfrac>
        </mfenced>
        <mi>x</mi>
      </msup>
    </mstyle>
    <annotation encoding="wiris">{&quot;version&quot;:&quot;1.1&quot;,&quot;math&quot;:&quot;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;msup&gt;&lt;mfenced&gt;&lt;mfrac&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mfrac&gt;&lt;/mfenced&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;/msup&gt;&lt;/math&gt;&quot;}</annotation>
  </semantics>
</math>

The given mathematical function is:

\[
f(x) = 3 \left( \frac{2}{3} \right)^x
\]

This is an exponential function where the base is \( \frac{2}{3} \) and the coefficient is 3. The function describes how the value of \( f(x) \) changes as \( x \) changes.

Would you like to explore the behavior of this function further, or would you like me to help you with a specific aspect of it?

### Related questions:
1. How do exponential functions behave for different values of the base?
2. What happens to the function when \( x = 0 \)?
3. How do you find the inverse of this function?
4. How can we graph this exponential function?
5. How do transformations like scaling and shifting affect exponential functions?

### Tip: Exponential functions like this one are used to model growth or decay in real-world situations, such as population growth or radioactive decay!

The given function is f(x) = 3(2/3)^x. How does this function behave?

Explore the behavior of the exponential function f(x) = 3(2/3)^x, including its properties, transformations, and real-world applications such as decay models. This detailed explanation is suitable for students in Grades 9-12.

Math Problem Statement

Solution

Related questions:

Tip: Exponential functions like this one are used to model growth or decay in real-world situations, such as population growth or radioactive decay!

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