Results 1 to 2 of 2

Math Help - Exponents word problem...

  1. #1
    Junior Member
    Joined
    Jan 2008
    Posts
    53

    Exponents word problem...

    Since January 1980, the population of the city of Brownville has grown according to the mathematical model y=720,500(1.022)^x, where x is the number of years since January 1980. Explain what the numbers 720,500 and 1.022 represent in this model. If this trend continues, use this model to predict the year during which the population of Brownville will reach 1,548,800.

    How do i figure this out?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,682
    Thanks
    614
    Hello, eh501!

    Since January 1980, the population of the city of Brownville has grown
    according to the mathematical model: y\:=\:720,\!500(1.022)^x
    where x is the number of years since January 1980.

    (a) Explain what the numbers 720,500 and 1.022 represent in this model.

    Let x=0 and we have: . y \:=\:720,\!500(1.022)^0 \:=\:720,\!500

    That is, when time is 0, the population was 720,500.

    Therefore, 720,500 is the initial population of the city (in 1980).


    The population is growing by a factor of 1.022 each year.
    This means that the population is growing by 2.2% annually.



    (b) If this trend continues, use this model to predict the year
    during which the population of Brownville will reach 1,548,800.

    Then question is: for what x will y = 1,\!548,\!000 ?

    We have: . 720,\!500(1.022)^x \:=\:1,\!548,\!000 \quad\Rightarrow\quad (1.022)^x \:=\:\frac{1,\!548,\!800}{720,\!500} \:=\:\frac{1408}{655}

    Take logs: . \log(1.022)^x \:=\:\log\left(\frac{1408}{655}\right) \quad\Rightarrow\quad x\cdot\log(1.022) \:=\:\log\left(\frac{1408}{655}\right)

    Hence: . x \;=\;\frac{\log(\frac{1408}{655})}{\log(1.02)} \;=\;35.16718012


    Therefore, the population will reach 1,548,800 during the 35th year (2015).

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Exponents Word Problem
    Posted in the Algebra Forum
    Replies: 8
    Last Post: September 28th 2011, 04:13 PM
  2. exponents word problem
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: September 25th 2011, 01:43 PM
  3. Problem with Exponents
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 27th 2009, 02:52 PM
  4. Word Problem w/exponents
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: November 18th 2007, 01:44 PM
  5. exponents problem
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: February 1st 2007, 05:25 AM

Search Tags


/mathhelpforum @mathhelpforum