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doombanana
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Homework Statement
The total amount of oil in a well is 24000 barrels. The present rate of consumption is 100 barrels per year. How long will the gas supply last if the present yearly rate of consumption increases by 1% per year?
Homework Equations
We can use the approximation [itex](1+x)^i = 1+xi[/itex] (1)
[itex]\sum i = \frac{n(n+1)}{2}[/itex] (2)
and the quadratic formula
The Attempt at a Solution
Using (1), the amount of oil left at any given year is [itex]y=24000-100(1+.01t)[/itex].
The sum of (2) should equal the total number of barrels (24000).
let [itex]n = 100+t[/itex] where t is the final year
substituting n into (2) gives
[itex]\frac{(100+t)^2 + (100+t)}{2} = 24000[/itex]
which gives
[itex] 0= t^2-201t-37900[/itex]
this gives a value of t= 119 years, but when I plug in my equation for y into Excel I get 142 years so I know I'm doing something wrong. Thank you for your help.