1. 20% The depth of a river flowing in a rectangular channel 10 m wide is measured over a period of 23 hours following a period of rain. The following table shows depth of the river in mm. 0 1 23 4 5 6 7 8 9 10 11 Time T (hours) Depth D (mm) 340 340 340 336 336 340 336 355 403 422 441 482 12 13 14 15 16 17 18 19 20 21 22 23 Time T (hours) Depth D (mm) 542 587 610 636 643 647 647 651 651 647 647 643 a) Using Excel plot a graph of this data, state the function representing the the 5th order polynomial line of best fit and show this on the graph. (For accuracy of the line of best fit function, constants should be expressed to 6 decimal places). 4% b) Comment on the differences between the actual data and the line of best fit function. 4% c) Differentiate the best fit function and find the rate (m/hour) at which the water is rising after 9 hours. 4% d) Determine the maximum river depth suggested by the best fit function and the time at which this occurs. 4% e) Integrate the best fit function between 1 and 23 hours to give an area (A) and multiply by the channel width (W) and velocity (V) (assumed to be 1m/s) to give the volume of water flowing in the 22 hour period. State the answer in cubic metres. Volume = A x W x V 4% 1. 20% The depth of a river flowing in a rectangular channel 10 m wide is measured over a period of 23 hours following a period of rain. The following table shows depth of the river in mm. 0 1 23 4 5 6 7 8 9 10 11 Time T (hours) Depth D (mm) 340 340 340 336 336 340 336 355 403 422 441 482 12 13 14 15 16 17 18 19 20 21 22 23 Time T (hours) Depth D (mm) 542 587 610 636 643 647 647 651 651 647 647 643 a) Using Excel plot a graph of this data, state the function representing the the 5th order polynomial line of best fit and show this on the graph. (For accuracy of the line of best fit function, constants should be expressed to 6 decimal places). 4% b) Comment on the differences between the actual data and the line of best fit function. 4% c) Differentiate the best fit function and find the rate (m/hour) at which the water is rising after 9 hours. 4% d) Determine the maximum river depth suggested by the best fit function and the time at which this occurs. 4% e) Integrate the best fit function between 1 and 23 hours to give an area (A) and multiply by the channel width (W) and velocity (V) (assumed to be 1m/s) to give the volume of water flowing in the 22 hour period. State the answer in cubic metres. Volume = A x W x V 4%