document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=142450>Question 142450</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780321361462/algebrahomeworkh>Mathematical Ideas</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am having problems trying to figure out what variable I have to solve for in these two problems. Could anyone please help me with these?  Thank you so much!<BR>\n" );
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document.write( "2. Assume the cost of a company picnic is described by the function<BR>\n" );
document.write( "P(n) = (1/2)n2 – 10n + 80\r<BR>\n" );
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document.write( "Where n represents the number of employees and family members attending the picnic and P (in dollars) represents the cost of the picnic.  How many employees and guests in attendance produce a minimum cost?  What is the minimum cost for this event?\r<BR>\n" );
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document.write( "3. In the formula N = Iekt, N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time.  There are currently 45 million cars in a certain country, increasing by 3.2% annually.  How many years will it take for this country to have 61 million cars.  Round to the nearest year. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103676 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=103676\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2. Assume the cost of a company picnic is described by the function<BR>\n" );
document.write( "P(n) = (1/2)n^2 – 10n + 80 \r<BR>\n" );
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document.write( "Where n represents the number of employees and family members attending the picnic and P (in dollars) represents the cost of the picnic. How many employees and guests in attendance produce a minimum cost? What is the minimum cost for this event? <BR>\n" );
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document.write( "You have quadratic function with a=1/2, b = -10 and c=80<BR>\n" );
document.write( "The lowest point, or minimum, occurs when n = -b/2a = 10/(2*(1/2)) = 10<BR>\n" );
document.write( "The minimum cost is P(10) = (1/2)10^2-10*10+80 = 50-100+80 = $30<BR>\n" );
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document.write( "3. In the formula N = Ie^(kt), <BR>\n" );
document.write( "N is the number of items in terms of an initial population I at a given time t and <BR>\n" );
document.write( "k is a growth constant equal to the percent of growth per unit time. <BR>\n" );
document.write( "There are currently 45 million cars in a certain country, increasing by 3.2% annually.<BR>\n" );
document.write( "How many years will it take for this country to have 61 million cars. Round to the nearest year.<BR>\n" );
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document.write( "61 million = (45 million)e^(0.032t)\r<BR>\n" );
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document.write( "1.356  = e^(0.032t)<BR>\n" );
document.write( "Take the natural log of both sides to get:<BR>\n" );
document.write( "0.032t = ln(1.356)<BR>\n" );
document.write( "t = 9.5168.. years<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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