Dow Jones Industrial Average The table shows the year-end closing prices p of the Dow Jones Industrial Average (DJIA) from 2000 through 2013, where t is the year, with
0 | 1 | 2 | 3 | |
10,786.85 | 10,021.50 | 8341.63 | 10,453.92 | |
t | 4 | 5 | 6 | 7 |
P | 10,783.01 | 10,717.50 | 12,463.15 | 13,264.82 |
t | 8 | 9 | 10 | 11 |
p | 8776.39 | 10,428.05 | 11,577.51 | 12,217.56 |
t | 12 | 13 | ||
P | 13,104.14 | 16,576.66 |
Spreadsheet at LarsonAppliedCaIculus.com
(a) Determine the average rate of change in the value of the DJIA from 2000 through 2013.
(b) Estimate the instantaneous rate of change in 2005 by finding the average rate of change from 2003 to 2007.
(c) Estimate the instantaneous rate of change in 2005 by finding the average rate of change from 2004 to 2006.
(d) Compare your answers for parts (b) and (c). Which interval do you think produced the best estimate for the instantaneous rate of change in 2005?
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