time (months) 0 1 2 3 4 5
rate pollutants are escaping (tons/month) 4 7 11 14 26 31
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?
Draw rectangles on this graph to help you overestimate the total pollutants that escaped during the first month. What overestimate did you obtain?
Draw rectangles on this graph to help you underestimate the total pollutants that escaped during the whole time. What underestimate did you obtain?
Draw rectangles on this graph to help you overestimate the total pollutants that escaped during the whole time. What overestimate did you obtain?
so, did you draw the rectangles?
What do you not understand?
I actually figured it out!!! Thank you anyways!
To sketch a smooth curve relating the two variables, follow these steps:
1. Draw a set of axes. The x-axis represents time in months, and the y-axis represents the rate of pollutants escaping in tons per month.
2. Plot the given data points on the graph. Connect the points with a smooth curve that represents the trend.
3. Ensure that the curve fits the data points as closely as possible.
To underestimate the total pollutants that escaped during the first month, draw rectangles as follows:
1. Draw a rectangle around the first data point, with the left side aligned with the y-axis and the top side aligned with the curve.
2. Extend the rectangle horizontally to the right until it reaches the next data point.
The underestimate can be calculated by finding the area of the rectangle. Multiply the width (in this case, the number of months) by the height (the rate of pollutants escaping). For the first month, the underestimate can be obtained by multiplying the width of one month (1) by the height at the beginning of the first month (4 tons/month).
To overestimate the total pollutants that escaped during the first month, draw rectangles as follows:
1. Draw a rectangle around the first data point, with the left side aligned with the y-axis and the top side aligned with the maximum value of the data points (31 tons/month in this case).
2. Extend the rectangle horizontally to the right until it reaches the next data point.
The overestimate can be calculated by finding the area of the rectangle. Multiply the width (in this case, the number of months) by the height (the maximum rate of pollutants escaping). For the first month, the overestimate can be obtained by multiplying the width of one month (1) by the maximum rate of pollutants escaping (31 tons/month).
To underestimate the total pollutants that escaped during the whole time, draw rectangles as follows:
1. Draw a rectangle around each data point, with the left side aligned with the y-axis and the top side aligned with the curve.
2. Extend each rectangle horizontally to the right until it reaches the next data point.
3. Sum the areas of all the rectangles.
The underestimate for the total pollutants that escaped during the whole time can be calculated by summing the areas of the rectangles. Multiply the width of each rectangle (the number of months between data points) by the height (the rate of pollutants escaping) and sum all the values.
To overestimate the total pollutants that escaped during the whole time, draw one large rectangle enclosing all the data points, with the left side aligned with the y-axis and the top side aligned with the maximum value of the data points.
Calculate the overestimate by finding the area of the large rectangle. Multiply the width of the rectangle (the total number of months) by the height (the maximum rate of pollutants escaping).
To sketch a smooth curve relating the two variables, you can plot the given data points on a graph. The x-axis represents time in months, and the y-axis represents the rate at which pollutants are escaping in tons per month. Connect the plotted points with a smooth curve.
Next, we will consider underestimating and overestimating the total pollutants that escaped during the first month using rectangles.
To underestimate the total pollutants that escaped during the first month, draw a rectangle with a base from the x-axis at month 0 to the x-axis at month 1. The height of the rectangle is the lowest value in the given data, which is 4 tons/month. Calculate the area of this rectangle, which is the underestimate of pollutants escaped in the first month.
To overestimate the total pollutants that escaped during the first month, draw a rectangle with a base from the x-axis at month 0 to the x-axis at month 1. The height of the rectangle is the highest value in the given data, which is 7 tons/month. Calculate the area of this rectangle, which is the overestimate of pollutants escaped in the first month.
For underestimating and overestimating the total pollutants that escaped during the whole time, draw rectangles from the x-axis at month 0 to the x-axis at month 5. For underestimation, the height of the rectangle is the lowest value in the data (4 tons/month). For overestimation, the height is the highest value in the data (31 tons/month). Calculate the area of these rectangles to obtain the underestimation and overestimation of total pollutants escaped during the whole time.
Remember that these calculations are under- or overestimates based on rectangles drawn on the graph and may not represent the exact values.
By following this procedure, you can estimate the pollutant levels and their underestimation or overestimation using rectangles on the graph.