Problem

Nursing—Inpatient Healthcare: Countries have different procedures and philosophies in the...

Nursing—Inpatient Healthcare: Countries have different procedures and philosophies in the way they approach acute inpatient healthcare. The country with the longest average inpatient stay is Japan. The annual average number of days an acute inpatient stays in the hospital in Japan from 2000 to 2010 can be modeled by

f(x) = 0.07x2 − 1.33x + 24.8 0 ≤ x ≤ 10

where x represents the number of years since 2000 and f(x) represents the average number of days an acute inpatient stays in the hospital. (Source: Organization for Economic Cooperation and Development.)

(a) Evaluate dy for x = 9 and Δx = dx = 1 and interpret.


(b) Write the equation of the tangent line of f at x = 9 and evaluate the equation for the year 2014. Interpret this result.

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