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).

1 Answer | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.

We’ve answered 318,916 questions. We can answer yours, too.

Ask a question