See Examples 1, 2, 4 , and 5 as you do Exercise 51.The following table shows the consumer...

See Examples 1, 2, 4 , and 5 as you do Exercise 51.

The following table shows the consumer price index (CPI) for medical care in selected years:

(a) Let x = 0 correspond to 1950. Find the rule of a piecewise linear function that models these data—that is, a piecewise linear function f with f(0) = 15.1, f(30) = 74.9, and f(60) = 388.4. Round all coefficients in your final answer to one decimal place.

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(b) Graph the function f for 0 ≤ x ≤ 65.

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(c) Use the function to estimate the medical−care CPI in 2004.

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(d) Assuming that this model remains accurate after 2010, estimate the medical−care CPI for 2015.

Example 1

Graph the following function:

Example 2

Graph the function

Example 3

Figure 3.12, on the following page, shows the median sales prices (in thousands of dollars) of new privately owned one−family houses by region of the United States (northeast, midwest, south, and west) from the years 2005 to 2011.

Example 4

Figure 3.13 is the graph of the function f whose rule is f(x) = average interest rate on a 30−year fixed−rate mortgage for a new home in year x.