Nursing—Inpatient Healthcare: The country with the shortest average inpatient stay is Denmark. The annual average number of days an acute inpatient stays in the hospital in Denmark from 2000 to 2010 can be modeled by
f(x) = 0.01x2 − 0.11x + 3.8 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 = 10 and Δx = dx = 1 and interpret.
(b) Write the equation of the tangent line of f at x = 10 and evaluate the equation for the year 2014. Interpret this result.
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