A Study Indicates That X Months From Now, The Popu

MythMonkey

From: US
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A study indicates that x months from now, the population of a certain town will be increasing at the rate of 10 + 2sqrt(x) people per months. By how much will the population increase over the next 9 months.

 

Answer No.1

Anonymous

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As f(x) = 2x^(1/2) + 10 indicates the rate of change of thepopulation, integrating it gives the population itself. F(x) = indefinite integral = 2 * x^(3/2) / (3/2) + 10x + C where C is the constant of integration (which represents an initialpopulation) We're only interested in the build-up over the next 9 months, so wetake the definite integral from 0 to 9. This is conventiently equal to the difference.. F(9) - F(0) = ( 2 * 9^(3/2) / (3/2) + 10 * 9 + C ) - ( 2 * 0^(3/2) / (3/2) + 10* 0 + C ) = 2 * 9^(3/2) / (3/2) + 10 * 9 = 126

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