please help me write a piecewise function

Question

Job A: This job pays 1850. per month plus a bonus of 250. per month. bonus will be put in account(no interest) after you have worked for the company for 30 months you will receive bonus in a lump sum. At beginning of 31st. month, the 250. bonus will again be placed in an account until the end of 60 months.

 

Job B: This job pays 2250.00 per month, but offers no bonus.

 

Job C: This job pays 1700.00 per month and offers a one-time bonus of 21,250. at the end of 35 months.

 

Please help me write a piecewise function for each job.

 

Answer 1

Hi Tammy,

 

Let y = pay received in a given month

let x = number of the month

 

Job A

 

y = 1850                       x<30

 

y = 1850 + 7500             x = 30

 

y = 1850                        30<x<60

 

y = 1850 + 7500              x = 60

 

 

Job B

 

y = 2250            x>0

 

 

Job C

 

y = 1700       x<35 and x>35

 

y = 1700 + 21,250   x = 35

 

Answer 2

Hello Tammy -

 

Piecewise functions just have sections that don't connect. So If you think of a graph, with the y-axis being the income from the job and the x-axis is the months from some starting point (assume the same for each job) then the A job will be: (Let I(m) be the function total income as a function of m, months)

 

I(m) = 1850*m from 0 to 30 on the graph. (So after 30 months you have made 1850*30 or 55,500)

I(m) = 250*30 + 1850*m from 30 to 60 

I(m) = 2(250*30) + 1850*m from 60 to 90 etc. assuming the pattern continues. 

 

Job B:

 

I(m) = 2250*m

 

Job C:

 

I(m) = 1700*m from 0 to 35

I(m) = 1700*m + 21250 from 36 on.

 

 

If you graph them all on the same graph (you have to put in the pieces separately) you can see that some are better earlier, some are better later. 

 

Hope this helps.

 

Ken