Chapter 3.1, Problem 42E

National health expenditures The following table shows the $2024$ projected U.S. health expenditures of various types (both total and per capita.)

$\begin{array}{ccccc}\begin{array}{l}\text{Expenditure}\\ \text{Type}\end{array}& \begin{array}{l}\text{Hospital}\\ \text{care}\end{array}& \begin{array}{l}\text{Physician}\\ \text{\&}\text{clinical}\\ \text{services}\end{array}& \begin{array}{l}\text{Personal}\\ \text{health}\\ \text{care}\end{array}& \text{Prescriptions}\\ \text{Total}& \text{1755}\text{.1}& \text{1034}\text{.8}& \text{4550}\text{.1}& \text{564}\text{.3}\\ \text{(\$}\text{billions)}& & & & \\ \text{Per}\text{capita}& \text{5053}& \text{2979}& \text{13,099}& \text{1624}\\ \text{(dollars)}& & & & \end{array}$

Source: Centers for Medicare and Medicaid Services

Use the data to make a $2\times 4$ matrix $E$ with each column representing a type of health expenditure.

These costs are predicted to change by about $6.1\%$ for the next year. Assuming a $6.1\%$ change in all these expenditures, use a matrix operation to find the predicted $2025$ amounts, correct to the nearest tenth of a billion dollars for total amounts and the nearest dollar for per capita.