Problem

Health The following table shows the consumer price index (CPI) for medical care in select...

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

Year

Medical CPI

1950

15.1

1975

47.5

2007

351.05

(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(25) = 47.5, andf(57) = 351.05. Round all coefficients in your final answer to one decimal place.


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


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


(d) Assuming that this model remains accurate after 2007, estimate the medical-care CPI for 2012.

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