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    Hi,
    I was just wondering if someone could take a look at this question and take a look at how i worked it out and if they thought it looks right.

    The worlds total proved reserves of oil have recently been estimated at 1,200,000 million barrels. The worlds total consumpetion of oil this year is estimated to be about 31,025 million barrels. If consumption increases by 1.5% per annum, and no new sources are discovered, how many more years will the reserves last?

    1,200,000e^0.015t=31,025

    e^0.015t=1,200,000/31,025

    e^0.015t=38.68

    0.015t+ln38.68

    t=ln38.68/0.015

    t=244 years

    The answer I got was 244 years, does that look reasonable or am i doing completely the wrong thing?

    Thanks for your time
    xx
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    I think this is a GP and that your method is wrong.
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    There are quite a few things wrong with what you're doing. For a start, you seem to have got the division the wrong way round when going from line 1 to line 2... although it'd correct if you had e^{-0.015t} in line 1, which is what I'd expect if you actually needed to use e here (which you don't).

    You're given the decrease rate as a percentage, and in the first year this is 31025. In the second year this will be 31025×1.015, in the third it will be 31025×0.015², and so on... so you're looking for the lower bound on the year where 31025 + 31025 \times 1.015 + 31025 \times 1.015^2 + \cdots + 31025\times 1.015^{n-1} \ge 1200000... this is a geometric progression. You can use S_n = a\dfrac{1-r^n}{1-r} to solve it.
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    (Original post by stem01)
    Hi,
    I was just wondering if someone could take a look at this question and take a look at how i worked it out and if they thought it looks right.

    The worlds total proved reserves of oil have recently been estimated at 1,200,000 million barrels. The worlds total consumpetion of oil this year is estimated to be about 31,025 million barrels. If consumption increases by 1.5% per annum, and no new sources are discovered, how many more years will the reserves last?

    1,200,000e^0.015t=31,025

    e^0.015t=1,200,000/31,025

    e^0.015t=38.68

    0.015t+ln38.68

    t=ln38.68/0.015

    t=244 years

    The answer I got was 244 years, does that look reasonable or am i doing completely the wrong thing?

    Thanks for your time
    xx
    Why are you using e ? I get approx 30 years
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    (Original post by steve2005)
    I hesitate but shouldn't it be 1.015
    No reason to hesitate, it should be 1.015 :p: Sorry, I just woke up.
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    Yeah, you don't really use e here (the question will probably give you an equation for e anyway, if e is required)
 
 
 
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