Results 1 to 4 of 4

Math Help - Population models.

  1. #1
    Newbie
    Joined
    Oct 2011
    Posts
    17

    Population models.

    So working on a exp growth word problem. I see the function should be P(t) = P0e^kt

    however they give me a function in the problem already

    f(t) = 100,000/(1+5000e^-t)

    so when solving should I just use the function they gave me instead of the P(t) = ?

    they want initial start of population, population after 4 weeks, and how many weeks to reach 40,000

    I get this for the first

    1) f(t) = 100,000/(1+5000e^0) = 100,000/5001
    2) f(t) = 100,000/(1+5000e^4) = correct form to put into calcualtor?
    3) this is where we need to solve for t correct?

    im completly lost on how to solve for t. I know 1^-x = 1/x..but will this work for e^-1 or should I just move it in front. blah :/
    Last edited by mr fantastic; October 20th 2011 at 04:41 AM. Reason: Moved from original thread.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member Youkla's Avatar
    Joined
    Oct 2011
    Posts
    26

    Re: Population models.

    Quote Originally Posted by RYdis View Post
    So working on a exp growth word problem. I see the function should be P(t) = P0e^kt

    however they give me a function in the problem already

    f(t) = 100,000/(1+5000e^-t)

    so when solving should I just use the function they gave me instead of the P(t) = ?

    they want initial start of population, population after 4 weeks, and how many weeks to reach 40,000

    I get this for the first

    1) f(t) = 100,000/(1+5000e^0) = 100,000/5001
    2) f(t) = 100,000/(1+5000e^4) = correct form to put into calcualtor?
    3) this is where we need to solve for t correct?

    im completly lost on how to solve for t. I know 1^-x = 1/x..but will this work for e^-1 or should I just move it in front. blah :/
    So you have \frac{100000}{(1+5000e^{-t})}

    For 1), you are correct...t=0
    For 2), it should be e^{-4}, not e^4

    e^{-t} = \frac{1}{e^t}, so for 3), set f(t) = 40,000, cross multiply and after you rearrange the data you should get e^{-t} = \frac{1.5}{5000}. Can you solve for t from there?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2011
    Posts
    17

    Re: Population models.

    Quote Originally Posted by Youkla View Post
    So you have \frac{100000}{(1+5000e^{-t})}

    For 1), you are correct...t=0
    For 2), it should be e^{-4}, not e^4

    e^{-t} = \frac{1}{e^t}, so for 3), set f(t) = 40,000, cross multiply and after you rearrange the data you should get e^{-t} = \frac{1.5}{5000}. Can you solve for t from there?
    not with any success yet :/

    I was able to come up with the same number after some one . but 1.5/5000 doesn't reallly give me a time frame for the answer. Answer 1 we were given t to solve for population, same with 2. 3 we are given population and told to find time. The first was intial time. So =0. Second was after 4 weeks. So t=4. However i can't see to use this information we have to get a week time frame. Maybe im missing something really obvious..sorry :/

    so I did e^-t = 1.5/5000 and changed to 1/e^t = 1/1.5/5000 = 5000/1.5 gives me around 3,333. It just dont seem like the correct answer :/
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member Youkla's Avatar
    Joined
    Oct 2011
    Posts
    26

    Re: Population models.

    So we have this:
    e^{-t} = \frac{1.5}{5000}

    This can then be re-written as
    \frac{1}{e^t} = \frac{1.5}{5000}

    From here we can then take the reciprocals of each and get
    e^t = \frac{5000}{1.5}

    Then to solve for t you take the natural log of both sides (have you learned this?). So you get
    \ln({e^t}) = \ln({\frac{5000}{1.5}})

    then

    t = \ln({\frac{5000}{1.5}})\approx{8.1} weeks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Population Models
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: October 20th 2010, 04:02 AM
  2. Population Models
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: May 24th 2009, 01:39 AM
  3. Help with population models question
    Posted in the Advanced Math Topics Forum
    Replies: 8
    Last Post: June 6th 2008, 05:00 AM
  4. models for population growth!!..HELPP!!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 3rd 2007, 06:43 AM
  5. Replies: 2
    Last Post: July 17th 2007, 05:11 AM

Search Tags


/mathhelpforum @mathhelpforum