document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=601881>Question 601881</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I have this question on a past paper for my exams which I am struggling with;\r<BR>\n" );
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document.write( "\"A gourmet chef is renowned for her spherical shaped souffle. Once it's put in the oven, its volume increases at a rate proportional to its radius.\r<BR>\n" );
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document.write( "Show that the radius r cm of the souffle, at time t minutes after it has been put in the over, satisfies the differential equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dr%2Fdt=k%2Fr ALIGN=MIDDLE  ALT=\"dr%2Fdt=k%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > where k is constant.\"\r<BR>\n" );
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document.write( "Thank you :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #380173 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=380173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"its volume increases at a rate proportional to its radius\"\r<BR>\n" );
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document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{dV}{dt} = Cr\"> where C is a constant. However we also know that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE V = \frac{4}{3}\pi r^3 \Rightarrow \frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}\">\r<BR>\n" );
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document.write( "because the souffle is shaped like a sphere. Substitute into the first equation to obtain\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE 4\pi r^2 \frac{dr}{dt} = Cr\">\r<BR>\n" );
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document.write( "Solve for dr/dt\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{dr}{dt} = \frac{C}{4\pi r} = \frac{k}{r}\"> (k is another constant). </SPAN>\n" );
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