Concept explainers
(a.)
A model for the total number of hospital beds in U.S. hospitals.
It has been determined that the model for the total number of hospital beds in United States from 1980 to 2002, is given as
Given:
The number of hospitals in the United States from 1980 to 2002 is given as,
The average number of hospital beds in each hospital from 1980 to 2002 is given as,
Here,
Concept used:
The total number of hospital beds is the product of the average number of hospital beds in each hospital and the total number of hospitals.
Calculation:
The number of hospitals in the United States from 1980 to 2002 is given as,
The average number of hospital beds in each hospital from 1980 to 2002 is given as,
Then, it follows that the total number of hospital beds from 1980 to 2002 is given as,
Put the required values in the above expression to get,
Here,
This is the required model for the total number of hospital beds in United States from 1980 to 2002.
Conclusion:
It has been determined that the model for the total number of hospital beds in United States from 1980 to 2002, is given as
(b.)
The number of beds in the U.S. hospitals in 1995, according to the obtained model.
It has been determined that the number of beds in the U.S. hospitals in 1995, according to the obtained model, is
Given:
The number of hospitals in the United States from 1980 to 2002 is given as,
The average number of hospital beds in each hospital from 1980 to 2002 is given as,
Here,
Concept used:
The number of beds in the U.S. hospitals in 1995, according to the obtained model, can be determined by plugging in the required value of
Calculation:
As determined previously, in part (a), the model for the total number of hospital beds in United States from 1980 to 2002, is given as,
Then, the year 1995 is represented by
Put
Solving,
This implies that the number of beds in the U.S. hospitals in 1995, according to the obtained model, is
Since the number of beds must be a whole number, the obtained value can be rounded off to the nearest whole number to get the number of beds in the U.S. hospitals in 1995, according to the obtained model as
Conclusion:
It has been determined that the number of beds in the U.S. hospitals in 1995, according to the obtained model, is
(c.)
How the model changes if the number of hospital beds is required in thousands.
It has been determined that the model for the number of beds in the U.S. hospitals in thousands, is given as
Given:
The number of hospitals in the United States from 1980 to 2002 is given as,
The average number of hospital beds in each hospital from 1980 to 2002 is given as,
Here,
Concept used:
If the number of hospital beds is required in thousands, then the obtained model which gives the number of hospital beds in units has to be divided by thousand.
Calculation:
As determined previously, in part (a), the model for the total number of hospital beds in United States from 1980 to 2002, is given as,
If the number of hospital beds is determined in thousands, then multiplying it by thousand should give the number of hospital beds in units.
Then, the obtained model which gives the number of hospital beds in units should be divided by thousand to produce the model which gives the number of hospital beds in thousands.
So, the required model is,
Conclusion:
It has been determined that the model for the number of beds in the U.S. hospitals in thousands, is given as
Chapter 2 Solutions
EBK ALGEBRA 2
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