Health Services Employment The numbers of people, in thousands, employed in psychiatric and substance abuse hospitals for selected years from 1990 to 2009 are given in the table.
Year | People Employed (thousands) |
1990 | 113 |
2000 | 86 |
2004 | 92 |
2005 | 93 |
2006 | 98 |
2007 | 99 |
2008 | 102 |
2009 | 105 |
a. Fit a linear model to the 1990 and 2000 data, with x equal to the number of years after 1990.
b. Fit a power model to the 2004–2009 data, with x equal to the number of years after 1990.
c. Combine the results of parts (a) and (b) to form a piecewise function that models the number employed for the years 1990–2009.
d. Use the piecewise function to answer the following:
i. Find and interpret the output for x = 1995.
ii. When was the number employed 90,000, according to the model?
iii. If the model remains accurate, when will there be 120 thousand people employed in psychiatric and substance abuse hospitals?
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