The worst ecological disaster in U.S. history began on April 20, 2010, and was caused by an explosion in the oil rig Deepwater Horizon, which resulted in the deaths of 11 people and triggered a massive oil spill into the Gulf of Mexico. Estimates of the exact amount of the oil spilled vary based on the source, but it is clearly a function of the number of days n it lasted and the leak rate of the oil, estimated by the United States Geological Service (USGS) to be 504,000 gallons each day! The function u that estimates the amount of oil spilled in n days can be defined as u(n) = 504,000n gallons/day. ⒸU.S. Coast Guard photo To find out how much oil spilled the first month (30 days), let n = 30: u(30) = 504,000(30) = 15,120,000 gallons. According to BP's worse-case scenario, the amount of oil spilled in n days can be estimated by the function b(n) = 2.520n million gallons, while the function r(n) = 441,000n gallons represents the amount of oil that can be recovered in n days. (a) The function a(n) = b(n) r(n) represents the actual amount of oil that spilled into the Gulf daily. Find a(n). a(n) = million gallons (b) How many gallons were actually spilled into the Gulf over a 50-day period? million gallons
The worst ecological disaster in U.S. history began on April 20, 2010, and was caused by an explosion in the oil rig Deepwater Horizon, which resulted in the deaths of 11 people and triggered a massive oil spill into the Gulf of Mexico. Estimates of the exact amount of the oil spilled vary based on the source, but it is clearly a function of the number of days n it lasted and the leak rate of the oil, estimated by the United States Geological Service (USGS) to be 504,000 gallons each day! The function u that estimates the amount of oil spilled in n days can be defined as u(n) = 504,000n gallons/day. ⒸU.S. Coast Guard photo To find out how much oil spilled the first month (30 days), let n = 30: u(30) = 504,000(30) = 15,120,000 gallons. According to BP's worse-case scenario, the amount of oil spilled in n days can be estimated by the function b(n) = 2.520n million gallons, while the function r(n) = 441,000n gallons represents the amount of oil that can be recovered in n days. (a) The function a(n) = b(n) r(n) represents the actual amount of oil that spilled into the Gulf daily. Find a(n). a(n) = million gallons (b) How many gallons were actually spilled into the Gulf over a 50-day period? million gallons
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The worst ecological disaster in U.S. history began on April 20, 2010, and was caused by an explosion in the oil rig Deepwater Horizon,
which resulted in the deaths of 11 people and triggered a massive oil spill into the Gulf of Mexico. Estimates of the exact amount of the
oil spilled vary based on the source, but it is clearly a function of the number of days n it lasted and the leak rate of the oil, estimated
by the United States Geological Service (USGS) to be 504,000 gallons each day! The function u that estimates the amount of oil spilled
in n days can be defined as u(n) = 504,000n gallons/day.
To find out how much oil spilled the first month (30 days), let n = 30:
u(30) = 504,000 (30)
U.S. Coast Guard photo
a(n) :
According to BP's worse-case scenario, the amount of oil spilled in n days can be estimated by the function b(n) = 2.520n million.
gallons, while the function r(n) = 441,000n gallons represents the amount of oil that can be recovered in n days.
(a) The function a(n) = b(n) — r(n) represents the actual amount of oil that spilled into the Gulf daily. Find a(n).
million gallons
=
= 15,120,000 gallons.
(b) How many gallons were actually spilled into the Gulf over a 50-day period?
million gallons
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