The oil production of a company trebles every 10 years from 1980. The oil production was 0.2 million barrels per day as per the statistics released by the Petroleum Dvelopment in
1st January 1995.

A) Writte the necessary function for the above.
B) When will the oil production become 1 million barrels per day.
C) Convert the above function in to natural exponentil form.

What is 'trebles'? Do you mean 'triples'?

Yes I mean 3 times more

The general formula for a geometric sequence is T_n=ar^{n-1}

You then have the years to be taken into consideration: 1980, 1990, 2000. From 1980 to 1990, the productivity triples, and 1990 is when your second term occurs.

So, T_2 = 0.2 = a(3^{2-1}) (since the common ratio is '3')

You can solve for a, the first term and also the previous rate of production.

a = 0.2 / 3 = 0.067 = 1/15

Therefore, T_n = \frac{1}{15}(3^{n-1})

For the second part, replace T_n by 1 and solve for n.

I think my equation is already in the exponential form...

The original question implies a steady-growth scenario, in which the company's production increases at the same rate (let's call it g, for growth) each year.

If the company's production level is some amount P, in any arbitrary year, then their production level n years later would be

P(1+g)^n

Given that their production triples every ten years, we can adjust the previous model to say that for any production level P, ten years later the production level would be 3P; thus the general model for this situation is

P(1+g)^{10} = 3P

which quickly reduces to (1+g)^{10} = 3 .

Now take the 10th root of both sides to find the annual production growth rate g that creates the requisite 3-fold growth every ten years.

Can you run with it from here? Good luck, and I hope that helped out a li'l bit.

The general formula for a geometric sequence is

You then have the years to be taken into consideration: 1980, 1990, 2000. From 1980 to 1990, the productivity triples, and 1990 is when your second term occurs.

So, (since the common ratio is '3')

You can solve for a, the first term and also the previous rate of production.

a = 0.2 / 3 = 0.067 = 1/15

Therefore,

For the second part, replace T_n by 1 and solve for n.

I think my equation is already in the exponential form

Thanks my frenid to helping me.

The original question implies a steady-growth scenario, in which the company's production increases at the same rate (let's call it g, for growth) each year.

If the company's production level is some amount P, in any arbitrary year, then their production level and years later would be



Given that their production triples every ten years, we can adjust the previous model to say that for any production level P, ten years later the production level would be 3P; thus the general model for this situation is



Which quickly reduces to .

Now take the 10th root of both sides to find the annual production growth rate g that creates the requisite 3-fold growth every ten years.

Can you run with it from here? Good luck, and I hope that helped out a li'l bit.

Thanks a lot my frined , yes I think I can run with it now.. thanks a lot