document.write( "Question 301540: I have a word problem, the textbook question is \"There are 5400 ants in a colony. If there were 1200 ants in the colony 8 months ago, what is the monthly rate of growth?\"\r
\n" ); document.write( "\n" ); document.write( "I think the equation is written as \"5400=1200%28x%29%5E-8\" but I'm not sure. Either way, I still can't figure out how to solve it. Any help would be much appreciated!! \n" ); document.write( "
Algebra.Com's Answer #216210 by Alan3354(69443)\"\" \"About 
You can put this solution on YOUR website!
\"There are 5400 ants in a colony. If there were 1200 ants in the colony 8 months ago, what is the monthly rate of growth?\"
\n" ); document.write( "-----------------------
\n" ); document.write( "If the number increases linearly, it's (5400 - 1200)/8 = 525/month
\n" ); document.write( "-------------------
\n" ); document.write( "It's more likely to be an exponential increase, tho, with a constant growth.
\n" ); document.write( "5400 = 1200*e^rt (t in months)
\n" ); document.write( "e^(8r) = 5400/1200 = 4.5
\n" ); document.write( "8r = ln(4.5)
\n" ); document.write( "r = ln(4.5)/8 =~ 0.188
\n" ); document.write( "------------------------
\n" ); document.write( "If it's done on a monthly basis:
\n" ); document.write( "5400 = 1200(1 + r)^8
\n" ); document.write( "(1+r)^8 = 4.5
\n" ); document.write( "1+r = 4.5^(1/8)
\n" ); document.write( "r = 4.5^(1/8) - 1
\n" ); document.write( "r =~ 0.206845
\n" ); document.write( " \n" ); document.write( "
\n" );