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1829cef7-33f7-455c-8b99-9f006f8b4043.html
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<h4> Activity</h4>
<p>The cost, in dollars, to produce 1 watt of solar energy is a function of the number of years since 1977, \(t\).</p>
<p>From 1977 to 1987, the cost could be modeled by an exponential function \(f\). Here is the graph of the function.</p>
<p><img alt="A sheet of solar panels." src="https://k12.openstax.org/contents/raise/resources/fc18f868b9d9768cc0ff232f4b608bfb26081391" width="300"></p>
<p><img alt="Graph of a function on grid." class="img-fluid atto_image_button_text-bottom" height="285" src="https://k12.openstax.org/contents/raise/resources/a0f79653ec7d1fa67449d4d8872e608bcbc6e9a2" width="300"></p>
<br>
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<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="841120a8-9c83-4e21-bb44-32b3f4348fbc" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>What is the statement \(f(9) \approx 6\) saying about this situation?</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p> 9 years after 1977 (or in 1986), the cost in dollars for one watt of solar energy was about $6.</p>
</div>
</div>
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<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="426025f1-3186-4c94-8837-bfa8e5304a68" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li> What is \(f(4)\)? What about \(f(3.5)\)? What do these values represent in this context?</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(f(4) \approx 25\), and \(f(3.5) \approx 30\). These values represent the cost in dollars of 1 watt of solar energy in 1981 (4 years after 1977) and halfway through 1980 (3.5 years after 1977).</p>
</div>
</div>
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<br>
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<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="42c7ac30-f7fa-4938-bc71-d19ecde10d49" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li> When \(f(t)=45\), what is \(t\)? What does that value of \(t\) represent in this context?</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>2 years after 1977 (in 1979), the cost in dollars of 1 watt of solar energy was $45.</p>
</div>
</div>
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<br>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="79ca2c76-7a3a-451e-b53e-7c9ca25ab2a3" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li>By what factor did the cost of 1 watt of solar energy change each year? (If you get stuck, consider creating a table.)</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(\frac34\) or 0.75 </p>
</div>
</div>
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<br>
<h4>Video: Understanding Characteristics of Graphs</h4>
<p>Watch the following video to learn more about the characteristics of graphs: </p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><video controls="true" crossorigin="anonymous">
<source src="https://k12.openstax.org/contents/raise/resources/fd1b442820a507ecca84f874647c5a0400e67a8e">
<track default="true" kind="captions" label="On" src="https://k12.openstax.org/contents/raise/resources/f7798ff0bec0471a3774432cfe2076f02a1f6b0c" srclang="en_us">https://k12.openstax.org/contents/raise/resources/fd1b442820a507ecca84f874647c5a0400e67a8e
</video></div>
</div>
<br>
<br>
<p>An imaginary line that a function value will not touch or cross is called an <span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">asymptote</span>.</p>
<p>The value of the range that the function will never touch is called the <span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">horizontal asymptote</span>. </p>
<p>In the function graphed, the horizontal asymptote is \(y=0\).</p>