A population of 3000 bacteria is introduced into a culture and grows in number according to the formula

P(t)= 3000(1 + 3t/100+ t^2),

wheretis measured in hours. Find the rate at which the population is growing when t=1

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- Dec 4th 2008, 08:53 PMbeachbunny619Find the rate at which the population is growing
A population of 3000 bacteria is introduced into a culture and grows in number according to the formula

P(t)= 3000(1 + 3t/100+ t^2),

where*t*is measured in hours. Find the rate at which the population is growing when t=1 - Dec 4th 2008, 09:01 PMwoohoo
Well, the rate of which it's growing will be told by the derivative of the population equation.

so take the derivative of P(t):

P(t) simplified is: 3000+60t+3000t^2

derivative of P(t)=90+6000t

then plug in 1 for t

90+12000=12090

so when t=1 the population is growing at a rate of 62 bacteria per hour

(plug into calculator to check) - Dec 4th 2008, 09:06 PMbeachbunny619
- Dec 4th 2008, 09:07 PMwoohoo
- Dec 4th 2008, 09:18 PMmathishard33
i'm pretty sure to find the rate when t = 1 you take the derivative of the original function

so P'(t)=3000(3/100 + 2t)

and plug in t = 1 and get 6090 bacteria/hr

i think thats the answer, i was struggling with this today and someone showed me how to do it. so i just learned it... - Dec 4th 2008, 09:20 PMmathishard33