1. Write a function that describes the area of the water puddle on the floor as a function of its radius. Use function notation. 2. Write a function that represents the radius of the puddle at time . Use function notation.
3. What is the area of the puddle on the floor when the employees arrive at work at 7 am? Write a composition of functions to help you, and round your answer to the nearest whole number. Explain how you found your answer.
4. What function represents how much more water can be added to the bucket before it overflows? Explain how you solved this problem.
5. At around noon the store roof appears to have stopped leaking, so an employee removes the bucket that was catching the water and does not replace it. Overnight it begins to rain again, and water starts leaking from the ceiling onto the floor, again creating a circular puddle. The hole in the roof is larger this time, so at each time, t, in minutes, the radius of the puddle increases by 0.25 cm. Write a composition of functions to represent the area of the puddle as a function of time.
6. Look at the function you wrote for question