Results 1 to 2 of 2

Math Help - exponential growth

  1. #1
    Junior Member
    Joined
    Mar 2007
    Posts
    63

    exponential growth

    The population of fish in an isolated lake is decreasing by 10% per year due to acid rain. Thus, 10% of the fish present at the beginning of any year are lost by the end of the year. At this rate, how many years will it take for the fish population to drop to 25% of its current level?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,547
    Thanks
    539
    Hello, Harry!

    The population of fish in an isolated lake is decreasing by 10% per year due to acid rain.
    Thus, 10% of the fish present at the beginning of any year are lost by the end of the year.
    At this rate, how many years will it take for the fish population to drop to 25% of its current level?

    First, work out the general formula . . .

    Let P
    o = original number of fish (at t = 0).

    After the first year, 90% of the fish remain.
    . . There are: .(0.90)感
    o fish left.

    After the second year, there are: .(0.90)眺P
    o fish left.

    After the third year, there are: .(0.90)雪P
    o fish left.

    After the nth year, there are: .(0.90)^n感
    o fish left.


    When will this equal 0.25感
    o ?

    We have: . (0.90)^n感
    o .= .0.25感o

    Divide by P
    o: . (0.90)^n .= .0.25

    Take logs: . ln(0.90)^n .= .ln(0.25)

    . . and we have: . n損n(0.90) .= .ln(0.25)

    . . . . . . . . . . .ln(0.25)
    Hence: . n .= .---------- .= .13.1576...
    . . . . . . . . . . .ln(0.90)


    Therefore, it will take a little more than 13 years.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Exponential Growth
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 25th 2009, 09:52 PM
  2. exponential growth
    Posted in the Pre-Calculus Forum
    Replies: 0
    Last Post: November 6th 2008, 07:37 PM
  3. Exponential Growth
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 1st 2008, 08:17 AM
  4. Exponential Growth
    Posted in the Business Math Forum
    Replies: 1
    Last Post: September 10th 2008, 02:54 PM
  5. exponential growth help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 15th 2007, 04:16 PM

Search Tags


/mathhelpforum @mathhelpforum