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Math Help - exponential growth problem

  1. #1
    Member Mr Rayon's Avatar
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    exponential growth problem

    Enrolments at Parkrange Primary School have increased by 7% each year since 2001 when there were 342 students enrolled. How many students were enrolled at the school in 2005?
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  2. #2
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    I'm not amazing at math, but I'll give my crack at it.

    The formula for exponential growth, in general, is Final Amount = Initial Amount x (Rate + 1)^Time.

    Initial = 342.
    Rate = 7% = 0.07.
    Time = 4.

    Final Population = 342 x (0.07 + 1)^4 = 448.
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  3. #3
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    Quote Originally Posted by Mr Rayon View Post
    Enrolments at Parkrange Primary School have increased by 7% each year since 2001 when there were 342 students enrolled. How many students were enrolled at the school in 2005?
    Look at the information we know:

    in 2001 there were 342 students enrolled
    each year, there are 7% more students.

    The goal is to find the number of students enrolled in 2005, 4 years later.


    First, figure out what 7% of 342 is. Keep in mind 7% is the same thing as .07. Percentages can always be converted into fractions. Examples:

    25% = .25
    47% = .47
    1% = .01
    100% = 1


    To find 7% of 342, take the decimal form of 7% and multiply it by 342:
    (.07)(342) = 23.94" alt="
    (.07)(342) = 23.94" />

    So this means that roughly 24 new students join the school every year. If you look back at the original problem, we need to know how many students there will be in 2005, which is 4 years later. So, multiply 24 by 4 to get 96 students. It's important to understand that this means there will be 96 MORE students, not 96 students total.

    So, 96 + 342 = 438 students in 2005.


    However....

    The question might be implying that it increases by 7% consecutively every year. This would change the outcome of the problem, so I'll go through that as well.

    We showed that (342)(.07) = 23.94 ~ 24

    Now you can add that number onto the previous value to find the number of students in 2002:

    342 + 24 = 368

    Now, take 7% of this value and add that onto it to find the number of students in 2003:

    (367)(.07) = 25.69 ~ 26
    367 + 26 = 393 students in 2003


    And again, for 2004:

    (393)(.07) = 27.51 ~ 28
    393 + 28 = 421 students in 2004


    And again, for 2005:

    (421)(.07) = 29.47 ~ 29
    421 + 29 = 450 students in 2005



    So I have two different answers. I don't understand completely what the question is asking but you'll either end up with 450 or 438 students in 2005. The reason this is different is because in the first case, I took 7% of the students in 2001 and assumed the same rate of growth over the next 4 years. For the second example, I assumed that each year, the school had slightly more new students than it did last year.

    Hope this helped!
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  4. #4
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    It's dangerous to round so much. =p

    Beautiful Mind took the safer approach. Remember multiplication is commutative

    342*1.07*1.07*1.07*1.07
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