4c01be0f-f57a-406c-be9d-a88c1d2382c5.html

<h4>Warm Up Activity</h4>
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    <p>Jada received a gift of $180. In the first week, she spent a third of the gift money. She continues spending a third of what is left each week thereafter. </p>
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      <li>Which equation best represents the amount of gift money \(g\), in dollars, she has after \(t\)<em>&nbsp;</em>weeks? </li>
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      <li> \(g=180&minus;\frac{1}{3}t\) </li>
      <li> \(g=180 \cdot (\frac{1}{3})^t\) </li>
      <li>\(g=\frac{1}{3} \cdot 180^t\) </li>
      <li> \(g=180 \cdot (\frac{2}{3})^t\) </li>
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    <p>Enter your answer here:</p>
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    <p>Compare your answer:</p>
    <p>
      \(g=180 \cdot (\frac{2}{3})^t\)</p>
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      <li>Explain your reasoning.</li>
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    <p>Enter your answer here:</p>
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    <p>Compare your answer:</p>
    <ul>
      <li>Jada's initial gift is $180. Then, she spends a third \(\frac{1}{3}\) of the whole amount each week. This means that she has \(\frac{2}{3}\) left after each week because \(1 - \frac{1}{3} = \frac{2}{3} \) (the whole amount minus a third). </li>
      <li>When writing the equation, \(a = 180 \) because that is the starting amount she was given. Then, because she spends \(\frac{1}{3}\) each week, that means only \(\frac{2}{3}\) is leftover. so, \(b = \frac{2}{3}\). The equation that results is \(g = 180 \cdot (23)^t\).</li>
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