The table on the next page shows the amount of property damage (in dollars) due to automobile accidents in California in recent years. In this exercise we are interested in the total amount of property damage due to automobile accidents over the 8-year period from mid-2000 to mid- 2008, using the data for the 9 years.

 

a. One approach is to sum up the numbers in the second column, but only count half of the first and last numbers. Give the answer to this calculation.

b. Approximate the amount of property damage over the 8-year period 2000–2008 by taking the average of the left endpoint sum and the right endpoint sum. Explain why this is equivalent to the calculation done in part a.

c. Explain why the answer from part a is the same as using the trapezoidal rule to approximate the amount of property damage over the 8-year period 2000–2008.

d. Find the equation of the least squares line for this data, letting x = 0 correspond to 2000. Then integrate this equation over the interval [0, 8] to estimate the amount of property damage over this time period. Compare with your answer to part a.

Transcribed Image Text:

Year 2000 2001 2002 2003 2004 2005 2006 2007 2008 Property Damage ($) 309,569 317,567 335,869 331,055 331,208 330,195 325,453 313,357 278,986