Word Problem with Geometric Series

[Broo4075]

Homework Statement

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?

Homework Equations

Ʃar^n Geometric series

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.

 

[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?

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

 

[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

 

[Mark44]

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?

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

 

[Mark44]

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

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.