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Word Problem with Geometric Series

  1. Nov 24, 2013 #1
    1. The problem statement, all variables and given/known data
    The total reserves of a nonrenewable resource are 600 million tons. Annual consumption, currently 20 million tons per year, is expected to rise by 1% each year. After how many years will the reserve be exhausted?

    Part 2. Instead of Increasing by 1% each year, suppose consumption was decreasing by a constant percentage per year. If existing reserves are to never be exhausted, what annual percentage reduction in consumption is required?

    2. Relevant equations
    Ʃar^n Geometric series

    3. The attempt at a solution

    i know that the common ratio r=1.01
    I'm just not really sure how to write a geometric series summation to fit the problem.
    I also am having a difficult time starting part B.
  2. jcsd
  3. Nov 24, 2013 #2


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    Well, the first year the consumption, call it ##C## is ##600##. Next year it is ##600(1.01)##. Next year ##600(1.01)^2## and so on. What is it in year ##n##? What is the sum of those? Where exactly are you stuck?

    [Edit] Woops, I typed 600 instead of 20. Was in a hurry this morning I guess. :frown:
    Last edited: Nov 24, 2013
  4. Nov 24, 2013 #3
    i think it's 20(1.01)^n, which is then added up with all the previous terms, and that is supposed to equal 600. I am having issues figuring out what n should be
  5. Nov 24, 2013 #4


    Staff: Mentor

    First year consumption is 20 (million tons), rising by 1% each year.
  6. Nov 24, 2013 #5


    Staff: Mentor

    20(1.01)n would be the consumption after n years. You're going to have to write a sum to represent the total consumption in all of the years. You can write the sum either as a summation or in expanded form.

    Since you are learning about geometric series, there must be some presentation in your text about how to find the sum of a particular number of terms in a geometric series.
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