Question

The equation below is used to predict the cost of a hospital stay (y) from the number of days a patient is in the hospital (x). y=102.40+302.4x
If a person increases his stay by an additional 4 days, how much would the hospital bill increase?

Answer 1

Let the initial number of days the person stays in the hospital is 'x days', then the cost of hospital stay is given by:

y|x = 102.40 + 302.4x

Now, let the hospital stay of that person increases by 4 days to 'x+4' days, then the cost of hospital stay is given by:

y|(x+4) = 102.40 + 302.4(x+4)

Thus, the increases in the hospital bill is given by:

y|(x+4) - y|x = 102.40 + 302.4(x+4) - [102.40 + 302.4x]

= 102.40 + 302.4x + 302.4*4 - 102.40 - 302.4x

= 302.4*4

= 1209.6 [ANSWER]

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