SOLUTION: Bill has decided to eat a healthier diet by decreasing the amount of salt he eats. He has decided to allow himself 35,000 milligrams of sodium in the first week of a new diet. Each

Question 828231: Bill has decided to eat a healthier diet by decreasing the amount of salt he eats. He has decided to allow himself 35,000 milligrams of sodium in the first week of a new diet. Each week he will decrease the amount of sodium by 10%. How much sodium will he consume in the first 9 weeks of his new diet?
PLEASE HELP
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Bill has decided to eat a healthier diet by decreasing the amount of salt he eats. He has decided to allow himself 35,000 milligrams of sodium in the first week of a new diet. Each week he will decrease the amount of sodium by 10%. How much sodium will he consume in the first 9 weeks of his new diet?
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35000 + 0.9*35000 + 0.9^2*35000 + ... + 0.9^8*35000
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That is a geometric series.
S(n) = a[r^n - 1]/[r - 1]
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S(9) = 35000[0.9^9 -1]/[0.9 - 1] = 35000[-0.6126/-0.1]
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= 35000[6.1258] = 214,402.83 mg
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Cheers,
Stan H.
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