A population of bacteria is introduced into a culture. the number of bacteria P can be modeled by P=500 (1+4t / (50+t^2)) where t is time in hours. Find the rate of change in population when t=2 ... ?

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Campbell

Mathematics

7 September, 10:53

A population of bacteria is introduced into a culture. the number of bacteria P can be modeled by P=500 (1+4t / (50+t^2)) where t is time in hours. Find the rate of change in population when t=2 ... ?

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Rocco Cochran · Answer 1

P (t) = 500 (1+4t / (50+t^2))

P' (t) = 500 [ (50+t^2).4 - 4t. 2t] / (50+t^2) ^2

by the quotient rule

500 (-4t^2 + 200) / (t^2 + 50) ^2

Hence

P' (2) = 500. (-16 + 200) / 54^2 ~ = 31.6