OIL SPILL PROBLEM

Suppose an oil tanker in the Atlantic Ocean breaks up and begins to leak oil which expands in a circular pattern. Several measurements over a period of time show that the radius in meters of the spill is expanding at three times the square root of the time in minutes since the accident. From previous experience in clean up operations, the captain knows that the cost depends on the area of the spill and is $10,000 plus $200 times the area in square meters of spill.

1. Construct a function for the radius of the spill as a function of the time since the accident.

2. Construct a function for the area of the spill as a function of the radius.

3. Construct a function for the cost of the clean up as a function of the area.

4. Construct a composition of functions which represents the area as a function of time.

5. Construct a composition of functions which represents the cost of the clean up as a function of time.

6. Sketch the graph of the composition of functions which represents the cost as a function of time.

a) What is the cost after 10 minutes?

b) What is the cost after 40 minutes?