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UNO [17]
3 years ago
6

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 ...?
Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
6 0
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
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