You are Here: Home >< Maths

# Trouble with logs watch

1. 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?

xx
2. I think this is a GP and that your method is wrong.
3. 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 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 ... this is a geometric progression. You can use to solve it.
4. (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?

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

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: July 21, 2009
Today on TSR

### A-Level OCR Biology Unofficial Markscheme

Find out how you've done here

### 1,032

students online now

Exam discussions

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams