For the years from 2002 and projected to 2024, the national health care expenditures H, in billions of dollars, can be modeled by H = 1,500e0.053t where t is the number of years past 2000.† In what year are national health care expenditures expected to reach $4.0 trillion (that is, $4,000 billion)?

2019.

Step-by-step explanation:

We have been given that for the years from 2002 and projected to 2024, the national health care expenditures H, in billions of dollars, can be modeled by where t is the number of years past 2000.

To find the year in which national health care expenditures expected to reach $4.0 trillion (that is, $4,000 billion), we will substitute in our given formula and solve for t as:

Take natural log of both sides:

So in the 18.5 years after 2000 the expenditure will reach 4 trillion.

Therefore, in year 2019 national health care expenditures are expected to reach $4.0 trillion.

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