Question

Suppose that P(x) represents the percentage of income spent on health care in year x and I(x) represents income in year x. Determine a function H that represents total health care expenditures in year x.

The function H that represents total health care expenditures in year x is _______

Answer 1

The total health care expenditures in year x would be equal to the product of the percentage of income spent on health care (P(x)) and the income (I(x)) in year x. Therefore, the function H can be expressed as:

H(x) = P(x) * I(x)

This function takes into account both the amount spent on health care as well as the income level, providing a comprehensive representation of health care expenditures.

Answer 2

Explanation:

that depends on the result dimension of P(x).

if P(x) delivers the percentage in the form xx.xx%, then

H(x) = I(x) × P(x) / 100

if P(x) delivers the percentage in the form 0.xxxx, then

H(x) = I(x) × P(x)

very basically, the absolute amount of a percentage of a whole is the product between both (and divided by 100).

e.g.

let's say, the whole amount is $64,000.

and we need to know 10% of that.

10% of 64,000 is then

64,000 × 10 / 100 = 6,400

or

64,000 × 0.10 = 6,400

can you see the connection, and why both versions do the same ?