document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204990>Question 1204990</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Convert the equation f(t) = 116(0.69)^t to the form f(t) = ae^kt\r<BR>\n" );
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document.write( "Find a = ? and k = ?\r<BR>\n" );
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document.write( "Round off to three decimal places </SPAN>\n" );
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document.write( "a = 116 since it's the coefficient out front.<BR>\n" );
document.write( "Alternatively, plug in t = 0 to find f(0) = 116 in the first equation and f(0) = a in the second equation. That leads to a = 116.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+116%2Ae%5E%28kt%29 ALIGN=MIDDLE  ALT=\"f%28t%29+=+116%2Ae%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > rewrites to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29+=+116%2A%28e%5Ek%29%5Et ALIGN=MIDDLE  ALT=\"f%28t%29+=+116%2A%28e%5Ek%29%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The base is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ek ALIGN=MIDDLE  ALT=\"e%5Ek\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Set this equal to the base 0.69 and isolate k.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ek+=+0.69 ALIGN=MIDDLE  ALT=\"e%5Ek+=+0.69\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+ln%280.69%29 ALIGN=MIDDLE  ALT=\"k+=+ln%280.69%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-0.371 ALIGN=MIDDLE  ALT=\"k+=+-0.371\"   DISABLED_style= \"max-width:90%; height:auto;\" > approximately\r<BR>\n" );
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document.write( "<font color=red>Summary</font><BR>\n" );
document.write( "a = 116<BR>\n" );
document.write( "k = -0.317 approximately<BR>\n" );
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