document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=703248>Question 703248</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two neighboring towns have had population changes over a ten year period that follow exponential growth or exponential decay patterns.- The population of Town A was 50,000 in 1980. It has increased in population by approximately 5.1% per year.- The population of Town B was 100,000 in 1980. It has experienced a decrease in population of 8.1% per year.\r<BR>\n" );
document.write( "\n" );
document.write( "Part A: Write an exponential model to describe the population of Town A. Estimate the population in the year 1988.<BR>\n" );
document.write( "Part B: Write an exponential model to describe the population of Town B.<BR>\n" );
document.write( "Part C: Estimate the population of town B in the year 2005. Is this a good approximation? Explain why or why not.<BR>\n" );
document.write( "Part D: Which model represents exponential growth? Which is a model of exponential decay? Explain why exponential growth or exponential decay models can be used for this data.<BR>\n" );
document.write( "Part E: Approximately how many years would it take the population of Town A to double? Determine the solution algebraically.<BR>\n" );
document.write( "Part F: In how many years would the population of Town B decrease by 25%? Determine the solution algebraically.<BR>\n" );
document.write( "Part G: Determine the year when the towns would have approximately the same population. Use two different methods. Explain why using an algebraic method would be difficult here.\r<BR>\n" );
document.write( "\n" );
document.write( "Can someone please solve this, my brother is learning this concept right now, so I found this practice problem online for him, but I don't know the right answers. If I knew the right answers, I could better instruct him how to do it. Thanks so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #433389 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=433389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two neighboring towns have had population changes over a ten year period that follow exponential growth or exponential decay patterns.- The population of Town A was 50,000 in 1980. It has increased in population by approximately 5.1% per year.- The population of Town B was 100,000 in 1980. It has experienced a decrease in population of 8.1% per year. <BR>\n" );
document.write( "Part A: Write an exponential model to describe the population of Town A. Estimate the population in the year 1988.<BR>\n" );
document.write( "P(x) = 50,000*(1+0.051)^x where x is number of years after 1980<BR>\n" );
document.write( "P(8) = 50,000*(1.051)^8 is approximately 74,438<BR>\n" );
document.write( "--------------------------------------------------------<BR>\n" );
document.write( "Part B: Write an exponential model to describe the population of Town B.<BR>\n" );
document.write( "P(x) = 100,000*(1-0.081)^x<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "Part C: Estimate the population of town B in the year 2005. Is this a good approximation? Explain why or why not.<BR>\n" );
document.write( "P(5) = 100,000*(0.919)^5 = 65,551<BR>\n" );
document.write( "Looks good to me.<BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "Part D: Which model represents exponential growth?:::: A<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Which is a model of exponential decay?::: B<BR>\n" );
document.write( " Explain why exponential growth or exponential decay models can be used for this data.<BR>\n" );
document.write( "A is increasing exponentially ; B is decreasing exponentially.<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "Part E: Approximately how many years would it take the population of Town A to double? Determine the solution algebraically.<BR>\n" );
document.write( "Solve: (1.051)^x = 2<BR>\n" );
document.write( "x = log(2)/log(1.051) is approximately 14 years<BR>\n" );
document.write( "--------------------------------------------------------<BR>\n" );
document.write( "Part F: In how many years would the population of Town B decrease by 25%? Determine the solution algebraically.<BR>\n" );
document.write( "Solve (0.919)^x = 0.75<BR>\n" );
document.write( "x = log(0.75)/log(0.919) is more than 3 years and less than 4<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "Part G: Determine the year when the towns would have approximately the same population. Use two different methods. Explain why using an algebraic method would be difficult here.<BR>\n" );
document.write( "50,000(1.051)^x = 100,000(0.919)^x<BR>\n" );
document.write( "---<BR>\n" );
document.write( "(1.051/0.919)^x = 2<BR>\n" );
document.write( "x = log(2)/log(1.144) is approximately 5.165 or more than 5 years; less than 6<BR>\n" );
document.write( "===================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );