Chapter 5 Project

The Ozone Layer

The level of ozone in Earth's atmosphere has been closely watched since the 1970s, with the level of ozone depletion at the south pole a good indicator of global trends. One model of the region of polar depletion assumes the region is circular and that its radius, over a certain period of time, grows at a constant rate of $2.6$ kilometers per hour.

1. Write the area of the circle as a function of the radius r.

2. Assuming that t is measured in hours, that $t=0$ corresponds to the start of the annual growth of the hole, and that the radius of the hole is initially $0$ kilometers, write the radius as a function of time t.

3. Write the area of the circle as a function of time t.

4. What is the radius after $3$ hours?

5. What is the radius after $5.5$ hours?

6. What is the area of the circle after $3$ hours?

7. What is the area of the circle after $5.5$ hours?

8. What is the average rate of change of the area from $3$ hours to $5.5$ hours?

9. What is the average rate of change of the area from $5.5$ hours to $8$ hours?

10. Is the average rate of change of the area increasing or decreasing as time passes?