Maths question?

dibs101

Any help here would be appreciated guys,

Im sure this is quite simple but im scratchin my head here... i guess im missin some basic maths principle...

How long will my reserve last if i have an annual increase of 1.5%

Oil reserves today - 1333100 million barrels
Oil production per year - 29200 million barrels

As it stands 1333100 / 29200 = 45.6years at current rates of use.

If there is an annual increase of 1.5% in production,

Then thats 29200 x 1.015 'to the power of x' = 1333100.... is that correct?

How do I calculate this?

gerry87

Think of it as a sum of a geometric series so if it was a 1.5% increase with a 29200 unit oil production (X is your reserve today).

[LATEX]$X = 29200 + 29200(1.015) + 29200(1.015)^2 + 29200(1.015)^3 + ... + 29200(1.015)^n$ [/LATEX]

then use the sum of a geometric series formula. You want to find the n that makes this true, so

[LATEX]X = 29200*\left[\frac{(1-(1.015)^N)}{(1-1.015)}\right][/LATEX]

you'll have to solve the formula for N, the best way to do this is using logs, so it becomes.

[LATEX]N = \frac{ln(1-(X/29200)*(1-1.015))}{(ln(1.015))} [/LATEX]

Now set X=1333100

[LATEX]N = \frac{ln(1-(1333100/29200)*(1-1.015))}{ln(1.015)} = 35.04[/LATEX]

edit: put it into latex

dibs101

thanks for your response guys,

Just lookin at the results 35 seems like a more plausible answer as at current rates of use you get around 45 years, if production increases i assume this value will trend twords 35 as opposed to 200...

It is not a maths exam rather a renewable energy exam so although your answer does seem right gerry... i think the maths involved seems a bit beyond the course structure and i assumed I was missing somethin simple. Thanks for your help guys

rccaulfield

I'm startin again with maths sorry for stupid question- Why are you using 1.015% when 1.5% is in the question?

Fremen

It's not 1.015%, it's multiplication by 1.015.

If you think about it for a minute, you'll see that increasing a number by 1.5% is the same as multiplying it by 1.015, just as increasing a number by 70% is the same as multiplying it by 1.7.

rccaulfield

Fremen wrote: »

It's not 1.015%, it's multiplication by 1.015.

If you think about it for a minute, you'll see that increasing a number by 1.5% is the same as multiplying it by 1.015, just as increasing a number by 70% is the same as multiplying it by 1.7.

I needed the full minute but i got- Thanks!;)