Question

This past year Randy graduated from a prestigious university where he was heavily recruited by three large companies. His goal is to retire early and pursue other careers. Each company proposed very different compensation, or payment plans. The table below includes the three companies and the compensation plans they will give him if he meets his monthly performance goals.

Four for Fore, INC.
Starting Salary of $4000 with a monthly pay raise of $400

Square Peg Corp.
Starting Salary of $100 the first month, with an increase of $400 in month 2, to $900 in month 3, $1600 in month 4, and so on

DoubleMint Candy Co.
Starting Salary of $1 the first month, $2 the second month, $4 the third month, $8 the fourth month and so on.

Help Randy decide which job offer to take. In advising Randy, consider both monthly and cumulative earnings given that his major goal is early retirement. Represent each compensation table with a table, equation, and a graph to support your recommendation. Identify the function family used to model each plan and the reason for your decision.

Answer 1

To help Randy decide which job offer to take, we will compare the monthly and cumulative earnings for each company over time.

Company 1: Four for Fore, INC.
Starting Salary of $4000 with a monthly pay raise of $400

Month Monthly Earnings Cumulative Earnings
1 $4,000 $4,000
2 $4,400 $8,400
3 $4,800 $13,200
4 $5,200 $18,400
5 $5,600 $24,000
6 $6,000 $30,000
The monthly earnings for Four for Fore, INC. increase at a constant rate of $400 per month. The cumulative earnings increase at an increasing rate due to the constant increase in monthly earnings. The function used to model this plan is a linear function.

Company 2: Square Peg Corp.
Starting Salary of $100 the first month, with an increase of $400 in month 2, to $900 in month 3, $1600 in month 4, and so on

Month Monthly Earnings Cumulative Earnings
1 $100 $100
2 $500 $600
3 $900 $1,500
4 $1,600 $3,100
5 $2,500 $5,600
6 $4,400 $10,000
The monthly earnings for Square Peg Corp. increase at an increasing rate due to the increasing step size. The cumulative earnings increase at an increasing rate due to the increasing monthly earnings and step size. The function used to model this plan is an exponential function.

Company 3: DoubleMint Candy Co.
Starting Salary of $1 the first month, $2 the second month, $4 the third month, $8 the fourth month and so on.

Month Monthly Earnings Cumulative Earnings
1 $1 $1
2 $2 $3
3 $4 $7
4 $8 $15
5 $16 $31
6 $32 $63
The monthly earnings for DoubleMint Candy Co. increase at an increasing rate due to the doubling of the salary each month. The cumulative earnings increase at an increasing rate due to the exponential growth of monthly earnings. The function used to model this plan is an exponential function.

Based on the analysis above, we recommend that Randy take the job offer from Four for Fore, INC. This plan offers a steady and predictable increase in earnings, which makes it easier to plan for early retirement. The exponential growth in earnings of the other two plans could make it harder to plan for the future, as the monthly earnings are less predictable.