4630f2be-00aa-4cf8-a231-1a4728897166.html

<h3>Warm Up (5 minutes)</h3>
<p>This warm up encourages students to look closely at functions and articulate the ways in which they are similar or
    distinct. There are many possible responses to the question. Given their current work on exponential functions,
    students might be inclined to wonder if the equations define exponential functions, to look for a growth factor, or
    to think about the initial value of the function.</p>
<h4>Student Activity</h4>
<p>Which one doesn&rsquo;t belong?</p>
<p>\(f(n)=8 \cdot 2^n\)</p>
<p><strong>Answer: </strong>\(f\) is the only one that doubles when \(n\) increases by 1.</p>
<p>\(g(n)=2 \cdot 8^n\)</p>
<p><strong>Answer: </strong>\(g\) is the only one that does not have 8 for its vertical intercept.</p>
<p>\(h(n)=8+2n\)</p>
<p><strong>Answer:</strong>\(h\) is the only one that is not an exponential function.</p>
<p>\(j(n)=8 \cdot (\frac{1}{2})^n\)</p>
<p><strong>Answer:</strong> \(j\) is the only one that is not increasing.</p>
<h4>Activity Synthesis</h4>
<p>Invite students to share their responses. Highlight ideas that are important to this unit, for example, how the
    vertical intercept for each function can be identified, that \(j\) is a function involving exponential decay, etc.
    Encourage precision in students&rsquo; mathematical language, for instance, by reinforcing the use of terms such as
    <em>exponential</em>, <em>growth factor</em>, <em>initial amount</em>, <em>base</em>, <em>exponent</em>,
    <em>linear</em>, etc.</p>