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Math Help - Find the rate at which the population is growing

  1. #1
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    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
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  2. #2
    Newbie woohoo's Avatar
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    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)
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  3. #3
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    Quote Originally Posted by woohoo View Post
    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...
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  4. #4
    Newbie woohoo's Avatar
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    Quote Originally Posted by beachbunny619 View Post
    It should be some kinda decimal...
    humm...

    I'm not quite sure then.

    Sorry about that!

    Anyone else?
    Explain for the both of us?
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  5. #5
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    Quote Originally Posted by beachbunny619 View Post
    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...
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  6. #6
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    Quote Originally Posted by beachbunny619 View Post
    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
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