Results 1 to 2 of 2

Math Help - growth and decay

  1. #1
    Newbie
    Joined
    Oct 2007
    Posts
    14

    growth and decay

    I need help finding the formula for P(t)!!


    A population P=P(t) grows exponentially with P(3)=60 and P(6)=90. Find the formula for P(t), and find the population when t=10.

    I know how to do this but only when P(0) is given, which it is not in this case. Please give some hints = )
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,707
    Thanks
    626
    Hello, redpanda11!

    A population P(t) grows exponentially with: P(3)=60 and P(6)=90
    Find the formula for P(t)
    The function has the form: . P(t) \;=\;ae^{bt}

    From P(3) = 60, we have: . ae^{3b} \:=\:60 . [1]

    From P(6)=90, we have: . ae^{6b} \:=\:90 . [2]

    Divide [2] by [1]: . \frac{ae^{6b}}{ae^{3b}} \:=\:\frac{90}{60}\quad\Rightarrow\quad e^{3b} \:=\:1.5\quad\Rightarrow\quad 3b \:=\:\ln(1.5)

    .Hence: . \boxed{b \:=\:\frac{1}{3}\ln(1.5)}


    The function (so far) is: . P(t) \;=\;ae^{\left(\frac{1}{3}\ln15\right)t} \;=\;a\left(e^{\ln15}\right)^{\frac{1}{3}t}\quad\R  ightarrow\quad P(t)\:=\:a(1.5)^{\frac{1}{3}t}

    From P(3) = 60, we have: . a(1.5)^1 \:=\:60\quad\Rightarrow\quad 1.5a \:=\:60\quad\Rightarrow\quad\boxed{a \:=\:40}


    Therefore: . {\color{blue}\boxed{P(t) \;=\;40(1.5)^{\frac{1}{3}t}}}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Growth & Decay
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 18th 2010, 07:40 AM
  2. Decay and Growth
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 4th 2009, 03:46 PM
  3. Exponents Growth and Decay
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 21st 2009, 06:59 PM
  4. Growth and Decay
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 8th 2009, 07:18 PM
  5. Exponential Growth & Decay
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 11th 2007, 08:33 PM

Search Tags


/mathhelpforum @mathhelpforum