Results 1 to 2 of 2

Math Help - geometric and arithmetic sequences

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    3

    geometric and arithmetic sequences

    On an island the population of a species of insect (species A) is increasing geometrically, with a population of 25,000 in 1990 & an annual growth rate of 13.5%. Another species of insect (species B) is increasing in population arithmetically with numbers 37,000 in 1990 & an annual increment of 3500.

    1. determine the difference in the numbers of the 2 species for each year during a decade (up to 1999)
    2. In what year will species A be greater in number than species B? Assuming the growth rates remain fixed.

    A scientist has a mathematical model where the species can cohabit provided that they have equal numbers in the year 2000.

    3. If the growth rate in species A is to remain unchanged, what would the annual increment in species B need to be to achieve this?
    4. If the annual increment in species B is to remain unchanged, what would the growth rate in species A need to be to achieve this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,802
    Thanks
    1576
    1. You should know for an arithmetic sequence that

    t_n = t_0 + nd

    and for a geometric sequence that

    t_n = t_0r^n.


    So for species A, the population during year n is

    A_n = 25\,000\cdot 0.135^n

    and for species B, the population during year n is

    B_n = 37\,000 + 3500n.


    2. You want species A to be greater in number than species B, so

    25\,000\cdot 0.135^n > 37\,000 + 3500n.

    You will need to use technology to solve this inequality for n.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. help with arithmetic and geometric sequences
    Posted in the Algebra Forum
    Replies: 3
    Last Post: December 6th 2010, 10:02 AM
  2. Sequences (arithmetic/geometric)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 29th 2009, 04:58 AM
  3. Arithmetic and geometric sequences
    Posted in the Algebra Forum
    Replies: 2
    Last Post: August 25th 2009, 05:18 PM
  4. Arithmetic and geometric sequences.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: February 21st 2009, 11:53 AM
  5. Arithmetic and Geometric Sequences
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 25th 2008, 04:19 PM

Search Tags


/mathhelpforum @mathhelpforum