Important Instructions to the Student: Please note the process for submission of the following exercise.

1. All explanations must be typed.The supporting math work must be neat and suitable for copying or scanning.2. The assignment must have the heading MATHEMATICAL REASONING EXERCISE. 3. Multiple pages must be numbered and paper clipped, no staples.

MATHEMATICAL REASONING EXERCISE

Instructions:The following problem requires you to decide which job you will accept among three choices.There is no "correct" answer.You will decide which job is the best one for you from a financial standpoint and you will be graded on the correctness of your equations and on the clarity, accuracy and soundness of your reasoning.We will assume that all three jobs mentioned are equally appealing to you in all other aspects except those described in the problem.Also, for simplicity, it is assumed that no taxes or other deductions will apply to your monthly check.Your answer must be written in complete and grammatically correct sentences.You may use graphs and/or the equations you derive to justify your arguments.

PROBLEM - CHOOSING THE BEST JOB

You are a college freshman and have planned your academic career carefully.You will complete college and receive your Bachelor's degree in five years.You were fortunate to have found a part-time job that is guaranteed for the five years and that will allow you to pay your bills while in school. We will call this Job A.After working at Job A for 25 months you are offered two other jobs at the same time, Job B and Job C, both of which are guaranteed for the remaining time (35 months) you are in school.You must make a decision whether to stay with Job A or switch to Job B or Job C.The decision must be made right after the 25th month; it cannot be delayed.

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.

Job B:This job pays $2250 per month, but offers no bonus.

Job C:This job pays $1700 per month and offers a one-time bonus of $21,250 at the end of the 35 months.

Remember that your decision is to be made when you have worked at Job A for exactly 25 months.

YOUR ASSIGNMENT

Artifact 1: For each job, give the equation (function) that calculates the amount A of money earned after m months.Your answer should involve piecewise-functions.