# Word Problem with Geometric Series

1. Nov 24, 2013

### Broo4075

1. The problem statement, all variables and given/known data
The total reserves of a nonrenewable resource are 600 million tons. Annual consumption, currently 20 million tons per year, is expected to rise by 1% each year. After how many years will the reserve be exhausted?

Part 2. Instead of Increasing by 1% each year, suppose consumption was decreasing by a constant percentage per year. If existing reserves are to never be exhausted, what annual percentage reduction in consumption is required?

2. Relevant equations
Ʃar^n Geometric series

3. The attempt at a solution

i know that the common ratio r=1.01
I'm just not really sure how to write a geometric series summation to fit the problem.
I also am having a difficult time starting part B.

2. Nov 24, 2013

### LCKurtz

Well, the first year the consumption, call it $C$ is $600$. Next year it is $600(1.01)$. Next year $600(1.01)^2$ and so on. What is it in year $n$? What is the sum of those? Where exactly are you stuck?

 Woops, I typed 600 instead of 20. Was in a hurry this morning I guess.

Last edited: Nov 24, 2013
3. Nov 24, 2013

### Broo4075

i think it's 20(1.01)^n, which is then added up with all the previous terms, and that is supposed to equal 600. I am having issues figuring out what n should be

4. Nov 24, 2013

### Staff: Mentor

First year consumption is 20 (million tons), rising by 1% each year.

5. Nov 24, 2013

### Staff: Mentor

20(1.01)n would be the consumption after n years. You're going to have to write a sum to represent the total consumption in all of the years. You can write the sum either as a summation or in expanded form.

Since you are learning about geometric series, there must be some presentation in your text about how to find the sum of a particular number of terms in a geometric series.