Question 1074297: A employer who started a new business has promised his employees a minimum starting wage of $3 with an increase of $2 every 4 years. sketch a graph of wage as a function of time for 16 years. assume the wages take affect at the beginning of the year where the change is made. (hint: use a step function to represent the function.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your step function equations would be:
y = 3 for 0 <= x < 4
y = 5 for 4 <= x < 8
y = 7 for 8 <= x < 12
y = 9 for 12 <= x < 16
y = 11 for 16 <= x < 20
x represents the number of years of employment.
for example, when x = 4, the employee has been there a full 4 years and is entitled to an additional 2 dollars wage to make the total wage equal to 3 + 2 = 5.
your graph stops at x = 16 because that's the number of years being considered.
at x = 16, the wage will be 11 dollars.
a sketch of the step function is shown below:
the closed circle indicates the value of y is valid at that value of x.
an open circle indicates the value of y is not valid at that value of x.
for example, when x = 4, y = 3 is not valid anymore, but y = 5 is.
on the 16th year of employment, the employee is entitled to an additional 2 dollars wage and starts earning at a wage of 11 dollars.
at employment (x = 0), the employee starts earning a wage of 3 dollars.
at 4 years (x = 4), the employee starts earning a wage of 5 dollars.
at 8 years (x = 8), the employee starts earning a wage of 7 dollars.
at 12 years (x = 12), the employee starts earning a wage of 9 dollars.
at 16 years (x = 16), the employee starts earning a wage of 11 dollars.
x represents a full year of employment.
y represents the wage the employee is entitled to earn.
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