A huge oil spill unleashes about 20,311 barrels of oil in the gulf every hour. T

Question

A huge oil spill unleashes about 20,311 barrels of oil in the gulf every hour. The makes an expanding circular layer of oil on the surface of the water about 1/16 inches thick with the center being the source of the spill. Let R(t) represent the radius in miles and t hours after 4 pm, the growing radius of the oil spill can be modeled by: R(t)=1/2 sqaure root t+2.

1. At what time did the spill start (when was the radius 0?)

2. How many miles for 0 hours, half an hour, an hour, an hour and a half, 2 hours, 2 and a half hours, 3 hours, 3 and a half hours, 4 hours and 4 and a half hours (round 2 decimal places)?

3. If left unchecked, how long will it take the oil spill to reach 2 mile radius?

The nearest containment crew is on a coast 50 miles away. At 4 pm the containtment vessels head to the center of the spill but the quickest a containment ship can travel is 12 miles per hour.

4. What equation represents the distant D(t) in miles that the vessel is from the center of the spill t hours after 4 pm?

5. How many miles for  0 hours, half an hour, an hour, an hour and a half, 2 hours, 2 and a half hours, 3 hours, 3 and a half hours, 4 hours and 4 and a half hours?

6. When will the vessel get to the center of the spill?

7. To the nearest minute, find when the vessel will reach the outer edge of the oil spill. There should be 2 answers, please explain.

8. What's the radius of the oil spill at this time?

9. To manage this spill, a vessel is needed every 800 ft around the outer ring of the spill, how many vessels are needed?

Explanation / Answer

1) R(t) = 1/2 sqrt (t+2)

a) time when spill started

0 = 1/2 sqrt t + 2

-2 = 1/2 sqrt t

squaring both sides

4 = 1/4 (t+2)

16 = ( t+2)

t = 16 - 2

t = 12

spill started at 4 am in the morning

b) miles for 0 hours

R(t) = 1/2 sqrt (0) + 2 = 2 miles

for 1/2 hour

R(t) = 1/2 sqrt (1/2) + 2 = 2.35 miles

for 1 hour

R(t) = 2.5 miles

for 1 1/2 hour

R(t) = 2.61 miles

for 2 hours

R(t) = 2.71 miles

for 2.5 hours

R(t) = 2.79 miles

for 3 hours

R(t) = 2.87 miles

for 3.5 hours

R(t) = 2.94 miles

for 4 hours

R(t) = 3 miles

for 4.5 hours

R(t) = 3.06 miles

c) it will take 0 hours to spill 2 miles

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