document.write( "Question 821663: Cholera is an infectious disease caused by the bacterium Vibrio cholera. This bacteria is known to grow exponentially. If you begin with a laboratory sample of 100 bacteria at 12:00 noon, and measure that there are 400 bacteria in your sample at 1:00pm the same day, how many bacteria would you expect in your sample at 3:00pm? Round answer to nearest unit. \n" ); document.write( "
Algebra.Com's Answer #494317 by TimothyLamb(4379)\"\" \"About 
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\n" ); document.write( "f(t)= P*e^(tk)
\n" ); document.write( "where:
\n" ); document.write( "P = initial value
\n" ); document.write( "k = growth or decay factor per unit of time
\n" ); document.write( "t = time
\n" ); document.write( "---
\n" ); document.write( "at t=1 hour, f(1) = 400 bacteria
\n" ); document.write( "f(1) = 400 = 100*e^k
\n" ); document.write( "---
\n" ); document.write( "400/100 = e^k
\n" ); document.write( "4 = e^k
\n" ); document.write( "ln(4) = ln( e^k )
\n" ); document.write( "ln(4) = k
\n" ); document.write( "k = 1.3862944 growth factor per hour
\n" ); document.write( "---
\n" ); document.write( "at t=3 hours, f(3) = ?
\n" ); document.write( "f(3) = 100*e^(3k)
\n" ); document.write( "f(3) = 100*e^(3k)
\n" ); document.write( "f(3) = 100*64
\n" ); document.write( "---
\n" ); document.write( "answer:
\n" ); document.write( "at 3 pm expect 6400 bacteria
\n" ); document.write( "---
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