Question

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

Answer 1

i assume this means take the derivative and evaluate at 2 right?

Answer 2

i surmise that you are right

Answer 3

ick. quotient rule time

Answer 4

i did that but got some funky answer that was negative

Answer 5

okay, maybe the derivative is off

Answer 6

by the way the 1+4t isnt actually on top of the fraction. just the 4t is. sorry

Answer 7

just 4t on top right?

Answer 8

yes

Answer 9

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

Answer 10

derivative is
\[ \frac{-2000 (t^2-50))}{(t^2+50)^2}\]

Answer 11

what jamesj said.

Answer 12

you need the steps or clear?

Answer 13

i did my quotient rule backwards

Answer 14

yeah i think i got it now

Answer 15

lol common mistake
goes away with practice

Answer 16

i used to do it all the time in my other class, i took the same class in highschool, but i guess ive not had enough practice but it's the first time ive done it this whole assignment. :)