Questions: Use this data to sketch a smooth curve relating the two variables. Draw rectangles on the graph you drew to help you underestimate the total pollutants that escaped during the first month. What underestimate did you obtain? tons Draw rectangles on this graph to help you overestimate the total pollutants that escaped during the first month. What overestimate did you obtain? tons Draw rectangles on this graph to help you underestimate the total pollutants that escaped during the whole time. What underestimate did you obtain? tons Draw rectangles on this graph to help you overestimate the total pollutants that escaped during the whole time. What overestimate did you obtain? 76 tons

Solution Steps

The data points given in the table are:

• Time (months): 0, 1, 2, 3, 4, 5
• Rate pollutants are escaping (tons/month): 4, 11, 131, 17, (missing value)

To underestimate the total pollutants that escaped during the first month, we use the rate at the beginning of the interval, which is 4 tons/month. The time interval is 1 month.

\[ \text{Underestimate for the first month} = 4 \times 1 = 4 \text{ tons} \]

To overestimate the total pollutants that escaped during the first month, we use the rate at the end of the interval, which is 11 tons/month. The time interval is 1 month.

\[ \text{Overestimate for the first month} = 11 \times 1 = 11 \text{ tons} \]

To underestimate the total pollutants that escaped during the whole time, we use the rate at the beginning of each interval. The time intervals are 1 month each.

\[ \text{Underestimate for the whole time} = (4 \times 1) + (11 \times 1) + (131 \times 1) + (17 \times 1) = 163 \text{ tons} \]

Final Answer