Situation: Oil is leaking out of a container at a decreasing rate. The rate is measured hourly.

We want to estimate the amount of oil that has leaked out of the container during the time shown.

1. What is the maximum amount of oil that could have leaked out during the first hour?

 

 

 

2. What is the minimum amount of oil that could have leaked out during the first hour?

 

 

 

3. What is the maximum amount of oil that could have leaked out during the second hour?

 

 

 

4. What is the minimum for the second hour?

 

 

 

5. Answer questions 3 and 4 for the 3^rd and 4^th hours.

 

 

 

6. If you had to guess how much oil actually leaked out in the four hour interval, what would be your guess?

 

 

 

7. What is the maximum possible error in your guess from the actual value?

 

 

 

 

 

 

Suppose additional readings are obtained and compiled.

8. Recalculate your upper and lower estimates in light of this new information.

 

 

 

 

 

 

9. Make a new guess for the total amount of oil which has leaked out in the 4 hour interval and estimate the maximum possible error in your guess.

 

 

 

 

 

 

10. If readings were obtained for every 1/10 hour, by how much would your upper estimate exceed your lower estimate? What if readings were obtained for every 1/100 hour?

 

 

 

 

 

11. What if you had access to readings of the rate at every instant during the 4 hour interval?