# Find the rate at which the population is growing

• Dec 4th 2008, 08:53 PM
beachbunny619
Find 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 PM
woohoo
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 PM
beachbunny619
Quote:

Originally Posted by woohoo
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)

It should be some kinda decimal...
• Dec 4th 2008, 09:07 PM
woohoo
Quote:

Originally Posted by beachbunny619
It should be some kinda decimal...

humm...

I'm not quite sure then.

Anyone else?
Explain for the both of us?
• Dec 4th 2008, 09:18 PM
mathishard33
Quote:

Originally Posted by beachbunny619
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

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 PM
mathishard33
Quote:

Originally Posted by beachbunny619
It should be some kinda decimal...

well thats what i thought too but if its the instant growth rate, not the relative growth rate, then its usually a # larger than the answer to the non-derivative function