Oil is leaking from an oil tanker at the rate of 2, 500 gallons per day. At this

Question

Oil is leaking from an oil tanker at the rate of 2, 500 gallons per day. At this rate the radius of the circular slick of oil is increasing at a rate of 5 miles per day. a. Create a function, call it r(t), that models the radius of the circular slick of oil at a time, t, days after the beginning of the leak. That is, find an expression for r(t) r(t) Preview b. The area of a circle is given by the formula A = m2. Create a function, call it A(t), that models the area of the oil slick at time t. That is, find an expression for A[r(t)]. A(t) = [ c. To the nearest whole number, what will the area of the oil slick 2 days after the beginning of the leak? square miles d. If it costs $4, 000, 000 to clean the oil from each square mile of the ocean, what is the cost of this spill 2 days after the beginning of the leak? Answer in millions of dollars using your rounded answer from part c. in your calculations SD million

Explanation / Answer

a) dr/dt =5

dr = 5dt

r = 5t + c

at the start of the leak the radius of slick = 0 at t=0

thus, r=5t+0=5t

b) Area = pi(r(t))^2 = 25pi t^2

c) When t= 2 days

Area = 25pi* (4) = 100pi square miles

d)it costs $ 4 million to clean each square mile.

To clean 100pi square miles.

Cost = $ 400pi million

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