document.write( "Question 823913: A little more than 43 million households own dogs in the US. The rate of increase in dog ownership is 1.5% each year. Approximately how many households are expected to own dogs in 10 years, if this trend continues? \n" ); document.write( "
Algebra.Com's Answer #495982 by TimothyLamb(4379)\"\" \"About 
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\n" ); document.write( "y(t) = a * e^(kt)
\n" ); document.write( "---
\n" ); document.write( "where y(t) = value at time t
\n" ); document.write( "a = value at the start
\n" ); document.write( "k = rate of growth (when k > 0) or decay (when k < 0)
\n" ); document.write( "t = time (years in this case)
\n" ); document.write( "---
\n" ); document.write( "number of households with dogs 1-year from now:
\n" ); document.write( "43000000 * 1.15 = 49450000
\n" ); document.write( "---
\n" ); document.write( "y(1) = 49450000 = 43000000 * e^(k(1))
\n" ); document.write( "y(1) = 49450000/43000000 = e^(k(1))
\n" ); document.write( "ln( 49450000/43000000 ) = ln( e^k )
\n" ); document.write( "k = ln( 49450000/43000000 )
\n" ); document.write( "k = 0.13976194237515862651
\n" ); document.write( "---
\n" ); document.write( "y(10) = 43000000 * e^(10k)
\n" ); document.write( "y(10) = 173958983
\n" ); document.write( "---
\n" ); document.write( "answer:
\n" ); document.write( "in 10 years there should be about 173.958983 million households with dogs.
\n" ); document.write( "---
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