Question

Data from the Centers for Medicare and Medicaid Services indicates that the annual per capita out-of-pocket expenses for health care can be approximated by y=39.6x+543 dollars, where x is the number of years past the year 2000. When are the per capita out-of-pocket expenses for health care predicted to be $1400?

Answer 1

During the year 2021.

Explanation:

As we have a function that defines the annual per capita out-of-pocket expenses for health care, we can work with it.

Knowing that, we clear x (this is the number of years past the year 2000, so it will contain our desired information).

`y=39.6x+543\Leftrightarrow x=(y-543)/(39.6)`

Now, as we want to know when are the per capita out-of-pocket expenses for health care predicted to be $1400, and this total is our variable y, then

`x=(1400-543)/(39.6)\approx 21.6`

Finally, we know that x is the number of years past the year 2000, so the answer is that during the year 2021, the per capita out-of-pocket expenses for health care are predicted to be $1400.