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With U.S. Department of Health and Human Services data from 2002 and projected to 2024, the total public expenditures for health care H can be modeled by H = 1,500e0.053t where t is the number of years past 2000 and H is in billions of dollars. If this model is accurate, at what rate (in billions of dollars per year) will health care expenditures change in 2021? (Round your answer to one decimal place.) $ billion/year

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sqdancefan

Answer:

  242.0 billion dollars per year

Step-by-step explanation:

The rate of change of H(t) is the derivative of the function:

  H'(t) = 1500(0.053)e^(0.053t) = 79.5e^(0.053t)

Then, 21 years after 2000, the rate of change is expected to be ...

 H'(21) = 79.5e^(0.053·21) ≈ 242.0 . . . . billion dollars per year

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