document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194826>Question 1194826</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Suppose there are 350 million people in the US. If the annual birth rate is 2.3% and the annual death rate is 1.9%, what is the relative annual growth rate (r) of the US Population? \r<BR>\n" );
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document.write( "a) What will the projected US Population be in 2042 based on an exponential growth model (base e)? Give the model and explain what each part represents.\r<BR>\n" );
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document.write( "b) What will the projected US Population be in 2050?\r<BR>\n" );
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document.write( "c) What will the projected US Population be in 2100?\r<BR>\n" );
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document.write( "d) What would happen if birth and death rates were reversed? Clearly explain what type of model this becomes and how the graph changes. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848441 by </B><A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><B>ElectricPavlov(122)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ElectricPavlov><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=848441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Calculate the Relative Annual Growth Rate (r)**\r<BR>\n" );
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document.write( "* **Net Growth Rate:** <BR>\n" );
document.write( "    * Birth Rate - Death Rate = 2.3% - 1.9% = 0.4% <BR>\n" );
document.write( "    * Convert to decimal: 0.4% = 0.004\r<BR>\n" );
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document.write( "* **Relative Annual Growth Rate (r):** 0.4% or 0.004\r<BR>\n" );
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document.write( "**a) Projected US Population in 2042**\r<BR>\n" );
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document.write( "* **Exponential Growth Model:** <BR>\n" );
document.write( "    * P(t) = P₀ * e^(rt) <BR>\n" );
document.write( "        * where:<BR>\n" );
document.write( "            * P(t) is the population at time t<BR>\n" );
document.write( "            * P₀ is the initial population (350 million)<BR>\n" );
document.write( "            * r is the annual growth rate (0.004)<BR>\n" );
document.write( "            * t is the time in years<BR>\n" );
document.write( "            * e is the base of the natural logarithm (approximately 2.71828)\r<BR>\n" );
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document.write( "* **Calculate Population in 2042:** <BR>\n" );
document.write( "    * t = 2042 - 2024 = 18 years<BR>\n" );
document.write( "    * P(18) = 350,000,000 * e^(0.004 * 18) <BR>\n" );
document.write( "    * P(18) ≈ 376,129,370\r<BR>\n" );
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document.write( "* **Projected US Population in 2042: Approximately 376 million**\r<BR>\n" );
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document.write( "**b) Projected US Population in 2050**\r<BR>\n" );
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document.write( "* **Calculate Population in 2050:** <BR>\n" );
document.write( "    * t = 2050 - 2024 = 26 years<BR>\n" );
document.write( "    * P(26) = 350,000,000 * e^(0.004 * 26) <BR>\n" );
document.write( "    * P(26) ≈ 388,360,159\r<BR>\n" );
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document.write( "* **Projected US Population in 2050: Approximately 388 million**\r<BR>\n" );
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document.write( "**c) Projected US Population in 2100**\r<BR>\n" );
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document.write( "* **Calculate Population in 2100:** <BR>\n" );
document.write( "    * t = 2100 - 2024 = 76 years<BR>\n" );
document.write( "    * P(76) = 350,000,000 * e^(0.004 * 76) <BR>\n" );
document.write( "    * P(76) ≈ 474,344,170\r<BR>\n" );
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document.write( "* **Projected US Population in 2100: Approximately 474 million**\r<BR>\n" );
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document.write( "**d) Reversed Birth and Death Rates**\r<BR>\n" );
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document.write( "* **New Growth Rate:** 1.9% (death rate) - 2.3% (birth rate) = -0.4% or -0.004<BR>\n" );
document.write( "* **Model Becomes Exponential Decay:** The population would decrease over time. <BR>\n" );
document.write( "* **Graph Changes:** <BR>\n" );
document.write( "    * Instead of an upward curve (exponential growth), the graph would show a downward curve, indicating a declining population. \r<BR>\n" );
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document.write( "**Key Points:**\r<BR>\n" );
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document.write( "* The exponential growth model assumes a constant growth rate, which may not always be accurate in reality. <BR>\n" );
document.write( "* Factors like migration, changes in birth and death rates, and resource availability can influence population growth.<BR>\n" );
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