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<div class=3DSection1>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'><o:p>&nbsp;</o:p></b></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'><o:p>&nbsp;</o:p></b></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'><o:p>&nbsp;</o:p></b></p>

<p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b style=3D=
'mso-bidi-font-weight:
normal'>Current Events and Exponential Functions<o:p></o:p></b></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>With financial news making headlines these days, I tho=
ught
it would be interesting to apply current data to material we are covering in
class.<span style=3D'mso-spacerun:yes'>&nbsp; </span>The following data fig=
ures
were obtained on the Web on Friday, September 19, 2008.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<ul style=3D'margin-top:0in' type=3Ddisc>
 <li class=3DMsoNormal style=3D'mso-list:l0 level1 lfo2;tab-stops:list .5in=
'>The
     AIG bailout is estimated to cost $85 billion.</li>
 <li class=3DMsoNormal style=3D'mso-list:l0 level1 lfo2;tab-stops:list .5in=
'>According
     to latest figures, the national dept was roughly $9,650,904,000,000 at
     10:40 am Friday, September 19, 2008.</li>
 <li class=3DMsoNormal style=3D'mso-list:l0 level1 lfo2;tab-stops:list .5in=
'>At
     10:40 am Friday, September 19, 2008, the U.S. Census reported the <st1=
:country-region
     w:st=3D"on"><st1:place w:st=3D"on">U.S.</st1:place></st1:country-regio=
n>
     population to be 305,197,372.</li>
</ul>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>Based on this data, if we assume that these costs are
equally distributed to each person counted on the above U.S. Census report,
answer the following questions.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<ol style=3D'margin-top:0in' start=3D1 type=3D1>
 <li class=3DMsoNormal style=3D'mso-list:l1 level1 lfo3;tab-stops:list .5in=
'>What
     would your share of the AIG bailout be?</li>
</ol>

<p class=3DMsoNormal style=3D'margin-left:.25in'><o:p>&nbsp;</o:p></p>

<ol style=3D'margin-top:0in' start=3D2 type=3D1>
 <li class=3DMsoNormal style=3D'mso-list:l1 level1 lfo3;tab-stops:list .5in=
'>What
     would your share of the current national dept be?</li>
</ol>

<p class=3DMsoNormal style=3D'margin-left:.25in'><o:p>&nbsp;</o:p></p>

<ol style=3D'margin-top:0in' start=3D3 type=3D1>
 <li class=3DMsoNormal style=3D'mso-list:l1 level1 lfo3;tab-stops:list .5in=
'>If we
     assumed that this current dept amount grows continuously at a rate of =
3%
     per year, what would your share of this dept be in 5 years?</li>
</ol>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'mso-tab-cou=
nt:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><i
style=3D'mso-bidi-font-style:normal'>This is an exponential growth problem.=
<span
style=3D'mso-spacerun:yes'>&nbsp; </span>Use the formula A =3D Pe<sup>rt</s=
up>,
where A is the <o:p></o:p></i></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><i style=3D'mso-bidi-font-=
style:
normal'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </sp=
an><span
class=3DGramE>amount</span> owed after t years, P is your share of the dept=
, r is
the interest rate <o:p></o:p></i></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><i style=3D'mso-bidi-font-=
style:
normal'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </sp=
an>(<span
class=3DGramE>assume</span> .03) and t is years (use 5).<sup><o:p></o:p></s=
up></i></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><sup><span style=3D'mso-ta=
b-count:
1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></sup></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><o:p>&nbsp;</o:p></p>

<ol style=3D'margin-top:0in' start=3D4 type=3D1>
 <li class=3DMsoNormal style=3D'mso-list:l1 level1 lfo3;tab-stops:list .5in=
'>If you
     decide to pay your share of this dept. (amount from problem 2) off in =
40
     years, how much would you need to pay each month if the interest rate
     were5%?<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>Refer back=
 to
     the monthly payment formulas for loans found in problems 49-52 on page=
 298
     of the text.</li>
</ol>

<p class=3DMsoNormal style=3D'margin-left:.25in'><span style=3D'mso-tab-cou=
nt:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span><i
style=3D'mso-bidi-font-style:normal'>One method of computing a monthly paym=
ent M
on a load of L dollars over a <span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp; </span>period
of t years with an interest rate of r is the following:<o:p></o:p></i></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><i style=3D'mso-bidi-font-=
style:
normal'><o:p>&nbsp;</o:p></i></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><i style=3D'mso-bidi-font-=
style:
normal'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </sp=
an>M =3D
Lrk/12(k-1)<span style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>where k =3D (1 + r/12)<sup>12t<o:p></o:p></sup></i></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><i style=3D'mso-bidi-font-=
style:
normal'><sup><o:p>&nbsp;</o:p></sup></i></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><i style=3D'mso-bidi-font-=
style:
normal'><sup><o:p>&nbsp;</o:p></sup></i></p>

<p class=3DMsoNormal>Update: The above represents the &quot;good old
days.&quot;<span style=3D'mso-spacerun:yes'>&nbsp; </span>On May 6, 2009 our
dept. was $11,260,764,000,000 (and growing).<span
style=3D'mso-spacerun:yes'>&nbsp; </span>Our population was 306,132,653 (and
growing).</p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><i style=3D'mso-bidi-font-=
style:
normal'><span style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </sp=
an><o:p></o:p></i></p>

<p class=3DMsoNormal style=3D'margin-left:.25in'><i style=3D'mso-bidi-font-=
style:
normal'><o:p>&nbsp;</o:p></i></p>

<p class=3DMsoNormal><i style=3D'mso-bidi-font-style:normal'><o:p>&nbsp;</o=
:p></i></p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

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