Question

Someone help pleaseeee

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 effect at the beginning of the year where the change is made. (HINT : use a step function to represent the function.)

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Answer 1

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.

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.

Answer 2

The step function graph represents the wage increases from a starting wage of $3, with a $2 raise every 4 years, resulting in horizontal lines that step up at the beginning of the 4th, 8th, and 12th years.

Step-by-step explanation:

The student's question relates to sketching the graph of wage as a function of time based on given parameters by the employer. This can be represented using a step function. The wages start at $3 per hour and increase by $2 every 4 years. Therefore, for the first 4 years, the wage is $3 per hour, from years 4 to 8 it is $5 per hour, from years 8 to 12 it is $7 per hour, and from years 12 to 16 it is $9 per hour. The result is a graph that steps up every 4 years.

To sketch this graph, you would plot the wage on the y-axis and time in years on the x-axis. You start at $(0, 3)$ and draw a horizontal line to $(4, 3)$. At the 4-year mark, you step up to a wage of $5 and draw another horizontal line from $(4, 5)$ to $(8, 5)$ and so on. These lines should be drawn right up to but not including the point where the raise takes effect (at years 4, 8, 12), indicating that the increase happens at the beginning of those years.