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?
Thanks for your time
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.
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:
in year 2:
in year 3:
in year n:
So total consumed in n years is:
Now use the formula for the sum of a finite geometric series on this and solve for in:
.
CB