how do i write a piecewise function for this?...

Question

Job A: This job pays $1850 per month plus a bonus of $250 per month. However, you will not receive the bonus on a monthly basis. It will be placed into an account (paying no interest). After you have worked for the company for 30 months you will receive, in a lump sum, all the money in the account at that time. If you quit before 30 months, you will receive none of the bonus money. Then, beginning with the 31st month, the $250 bonus will again be placed into the savings account each month for the remaining time you work for the company. At the end of 60 months, you will receive, in a lump sum, the remaining bonus money. If you quit before 60 months, you will receive none of the bonus money that accumulated beginning with the 31st month.

Answer 1

Here we go, Evelyn.  Hopefully this answer will help you with the others!

 

Let's let m = the number of months. 

 

If I quit before 30 months, I get no bonus, so I receive $1850m

 

If I quit after 30 months but before 60 months, I receive $1850m + 30(250), because I get the first 30 months of bonus.

 

If I stay 60 months, then I get $1850m + 60(250).

 

I'm not sure how to type the big { so imagine it's there.

 

f(m) = $1850m                  if m < 30

           $1850m + $7500     if 30 < m < 60

           $1850 + $15,000     if m = 60

 

Hope this helps!