The population P, in thousands of a small city is given by P(t)= 300t/2t^2+9 where t=time, in months. Find the growth rate, P'(t).
The population P(t) of a town after t months is given by `P(t)= (300*t)/(2t^2+9)`
The growth rate `P'(t) = (300*(2t^2 + 9) - 300*t*4t)/(2t^2 + 9)^2`
=> `(600t^2 + 2700 - 1200t^2)/(2t^2 + 9)^2`
=> `(2700 - 600*t^2)/(2t^2 + 9)^2`
The growth rate of population is `(2700 - 600*t^2)/(2t^2 + 9)^2` thousand per month.
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