document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190860>Question 1190860</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the given information to find an exponential model of the form Q = Q0e−kt or Q = Q0ekt, as appropriate. Round all numerical values to three significant digits when rounding is necessary.<BR>\n" );
document.write( "Q is the amount of radioactive substance with a half-life of 160 years in a sample originally containing 7 grams (t is time in years).<BR>\n" );
document.write( "Q =  </SPAN>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q%5B0%5D+=+7 ALIGN=MIDDLE  ALT=\"Q%5B0%5D+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the original amount in grams.\r<BR>\n" );
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document.write( "We'll use the exponential decay model <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q+=+Q%5B0%5De%5E%28-kt%29 ALIGN=MIDDLE  ALT=\"Q+=+Q%5B0%5De%5E%28-kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "The negative exponent is what causes the decay.\r<BR>\n" );
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document.write( "The half-life is 160 years, which means at time t = 160, the initial amount is cut in half to 7/2 = 3.5 grams<BR>\n" );
document.write( "Plugging t = 160 leads to Q = 3.5\r<BR>\n" );
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document.write( "This is sufficient to help us find k<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q+=+Q%5B0%5De%5E%28-kt%29 ALIGN=MIDDLE  ALT=\"Q+=+Q%5B0%5De%5E%28-kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.5+=+7e%5E%28-k%2A160%29 ALIGN=MIDDLE  ALT=\"3.5+=+7e%5E%28-k%2A160%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.5%2F7+=+e%5E%28-160k%29 ALIGN=MIDDLE  ALT=\"3.5%2F7+=+e%5E%28-160k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5+=+e%5E%28-160k%29 ALIGN=MIDDLE  ALT=\"0.5+=+e%5E%28-160k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%280.5%29+=+-160k ALIGN=MIDDLE  ALT=\"ln%280.5%29+=+-160k\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-ln%280.5%29%2F160 ALIGN=MIDDLE  ALT=\"k+=+-ln%280.5%29%2F160\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+0.0043321698785 ALIGN=MIDDLE  ALT=\"k+=+0.0043321698785\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is approximate\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+0.00433 ALIGN=MIDDLE  ALT=\"k+=+0.00433\"   DISABLED_style= \"max-width:90%; height:auto;\" > when rounding to 3 sig figs. The three zeros aren't significant figures.\r<BR>\n" );
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document.write( "Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Q+=+7e%5E%28-0.00433t%29 ALIGN=MIDDLE  ALT=\"Q+=+7e%5E%28-0.00433t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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