document.write( "Question 1188373: 2. The population of a certain strain of bacteria is represented by the function g(t) = t^4+6t^3-t^2-6t, where t is in hours. How many bacteria will there be after 3 hours? How many hours will the population of the bacteria become 2520? \n" ); document.write( "

Algebra.Com's Answer #819445 by ikleyn(52866) $\"\"$ $\"About$

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document.write( "t^4 + 6t^3 - t^2 - 6t = factor by grouping = t^3*(t+6) - t*(t+6) = (t^3 - t)*(t+6) = t*(t^2-1)*(t+6).\r\n" );
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document.write( "5220 is divisible by 2 and by 3 (via the sum of digits), so it is divisible by 6.\r\n" );
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document.write( "So, try t = 6, and you will see that  6*(6^2-1)*(6+6) = 6*35*12 = 2520.\r\n" );
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document.write( "So, t= 6 hours is one of possible solutions.\r\n" );
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