SOLUTION: As an employee for the environmental protection agency, you have been to examine the pollution level in stinky pond. This pond holds 50,000 gallons of water and contains 20 pounds

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Question 142824: As an employee for the environmental protection agency, you have been to examine the pollution level in stinky pond. This pond holds 50,000 gallons of water and contains 20 pounds of pollution. The pollution is dissolved in the pond and is evenly distributed throughout. Each week. Half of the polluted water pours out of the pond and is replaced by equivalent amount of rainwater containing 5 pounds of pollution.
How much pollution remains in the pond after 267 weeks?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Day 1: 20 lbs of pollution
Day 2: (1/2)20 + 5 = 15 lbs of pollution
Day 3: (1/2)[(1/2)20 + 5] + 5 = (1/2)^2*20 + (1/2)5 + 5
Day 4: (1/2)[(1/2)^2*20 + (1/2)5 + 5] = (1/2)^3*20+ (1/2)^2*5 +(1/2)5 + 5
Day 5: (1/2)[(1/2)^3*20+ (1/2)^2*5+(1/2)5]+5 = (1/2)^4*20+(1/2)^3*5+(1/2)^25 + 5
.....
Day 267: (1/2)^266*20 + (1/2)^265*5 + (1/2)^264*5 + ... + 5
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Cheers,
Stan H.