PLEASE HELP WITH THIS CALC PROBLEM

Question

Oil is leaking from an oil tanker at 

the rate of 3,500 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, r days after the beginning of the leak. That is, find an expres-sion for r (t).

b. The area of a circle is given by the formula A = πr 2. Create a function, call 

it A(t), that models the area of the oil slick at time t. That is, find an expres-sion for A[r(t)].

c. To the nearest whole number, what will be the area of the oil slick 2 days 

after the beginning of the leak?

d. If it costs $5,000,000 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 1

Is the tank a sphere, cylinder or cone...

Oil is leaking at a rate of 3500 per day...

dV/dt = -3500

Radius is increasing 5 miles per day...

a) dR/dt = 5 ---> R = 5t + C

b) A = pi * R^2 = pi ( 5t+C)^2

= pi (25t^2 + 10C t + C^2)

dA/dt = 2 * pi * R * dR/dt

c) t=2 --> A = pi ( 100 + 20C + C^2)

d) 5 million times pi * R(t)^2

Answer 2

3500 g/d

r=5m/d

r^2pi=3500; r=33.379.......

" " =7000; r=47.203........

" " =10500; r=57.812....

47203-33379=13824

/ 33379

=41.415%

57812-47203=10609

/ 47203

=22.47%