# Math Help - Quick Question logs

1. ## Quick Question logs

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?

xx

2. Originally Posted 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?

xx
How much oil will be used in 244 years at 31,025 Million Barrels per year with no growth in consuption?

Is this more or less than the current proven reserves?

CB

3. Oh so by putting 244 into the equation I can see?

31025e^0.015x244 = 1,205,673

This is 5673 above the worlds oil reserves

Am i doing the right thing?

Thanks
xx

4. Originally Posted 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=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?

xx
I had already written "No, that's completely wrong! Where did you get that formula?" until I realized you are using an exponential approximation. I did it by writing it as 31.025(1+ 1.015+ 1.015^2+ ...+ 1.015^n)= 1200000 and using the formula for the sum of a finite geometric series and got 243 years! Yes, your answer is reasonable.

5. In 244 years - without the consumption increase - 7,570,100 million barrels would be consumed. So I would say that your answer doesn't look reasonable.

6. Oh i see. Would you be able to point me in the right direction in what to do.

Thanks
xx

7. Originally Posted 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?

xx
What are you trying to do, none of the above makes any sense.

Please explain what you are doing at each step (and as a reality check the proven reserves will be exhausted in less then 40 years at current consumption).

CB

8. Originally Posted by Stem01
Oh i see. Would you be able to point me in the right direction in what to do.

Thanks
xx
A bit tricky since useless you do this using a spreadsheet program calculating the consumption each year and summing them until the total exceeds 1200000 barrels, this is most easily done using calculus, though I suppose you could use a geometric series approach.

consumption in year 1: $c(1)=31025$

in year 2: $1.015 c(1)$

in year 3: $1.015^2 c(1)$

in year n: $1.015^n c(1)$

So total consumed in n years is:

$C(n)=c(1)\times 1.015[1+1.015+1.015^2+...+1.015^{n-1}]$

Now use the formula for the sum of a finite geometric series on this and solve for $n$ in:

$C(n)=1200000$.

CB