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<quiz>
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    <name>
      <text>6.1.3.2 Exponential growth of a fuction</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p><p></p><p>A function \(f(x)\) grows exponentially and is such that \(f(0)=1\) and \(f({@pp@})={@aa@}\). Find the exponential curve that fits through these points. Assume the function is \(f(x)=e^{kx}\) where \(k\) is to be determined from the given information. Find the value of \(k\) up to 3 d.p.</p><p>Hint: First try values \(&nbsp;{@dd11@},{@dd12@},&nbsp;{@dd13@} \)<br></p><p>\(k = \) [[input:ans1]] [[validation:ans1]]</p>]]></text>
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    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2020081700</text>
    </stackversion>
    <questionvariables>
      <text>aa: rand(10)+2;
pp: rand(4)+2;
dd11: decimalplaces(float(log(aa)/pp-0.1),1);
dd12: decimalplaces(float(log(aa)/pp),1);
dd13: decimalplaces(float(log(aa)/pp+0.1),1);
dd2: decimalplaces(log(aa)/pp,2);
dd3: decimalplaces(log(aa)/pp,3)</text>
    </questionvariables>
    <specificfeedback format="html">
      <text>[[feedback:prt1]]</text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\( k={@dispdp(dd3,3)@} \)</text>
    </questionnote>
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      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>dot</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
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      <name>ans1</name>
      <type>numerical</type>
      <tans>dd3</tans>
      <boxsize>10</boxsize>
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        <answertest>NumDecPlaces</answertest>
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        <name>1</name>
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        <answertest>NumAbsolute</answertest>
        <sans>ans1</sans>
        <tans>dd3</tans>
        <testoptions>0.002</testoptions>
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    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>dispdp(dd3,3)</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-2-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>log(aa)/pp</value>
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        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
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        <expectedanswernote>prt1-1-F</expectedanswernote>
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  </question>
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