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STEP FUNCTIONS
131
The total price of a long-distance phone call as a function of its length 
when the fee is 12 cents per minute or any fraction thereof.

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It is easier to charge someone for partial time or expense than to give that person
an added bonus.
A case in which expense is rounded down is in the payment of hourly wages.
If an employee works 40.7 hours in a week, then he or she might only get paid
for 40 hours time, since she did not put in a full 41 hours. A step function is used,
because it is easier to pay employees at an hourly rate than a minute rate, as well
as to encourage employees to follow a tight schedule. In this situation, the step
function that rounds down is called a floor function, or the greatest integer func-
tion. If the employee earns $12 per hour, then his or her weekly salary payment
in dollars, 
s, as a function of the number of hours worked, h, is s = 12[h]. The
[h] is the symbol to represent the greatest integer value of h, which in essence
rounds the value down to the nearest integer. This equation can equivalently be
written as 
s = 12
⌊h⌋ or s = 12 floor (h) so that they include symbols describ-
ing the floor function.
A floor function has also been used to identify the day of the week for any
date on the calendar since 1582. The remainder of the division in the equation 
w =
d+2m+

3(m+1)
5

+y+

y
4

−

y
100

+

y
400

+2
7
is used to predict the day of the week, 
w, where Sunday is the first day of the week
and Saturday is the seventh or zero day. The variable 
d represents the day of the
month,
m represents the number of the month, and y represents the year. An
exception to the value of 
m is in January and February, which are the month num-
bers according to the previous year. That means that January is represented by 13,
February by 14, March by 3, April by 4, and so on. For example, February 16,
1918 occurred on a Tuesday, because the remainder is equal to 3 when 
d = 14,
m = 16, and y = 1918 are substituted into the equation.
online sources for further exploration
Calendars


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Houston Lighting and Power calculator 

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Telephone rate calculator 

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