- I'll think about it then tell you.
- Hello. Would you like to take a full time job for the month of April? You will get paid a penny on the first day. Everyday I will double your pay from the day before.
- SunMonTuesWednesThursFriSaturTotal.1.2.4.8.16.32.641.271.282.565.1210.2420.4840.9681.92163.83
- I'll make $1.27 in the first week. In two weeks i will have made $163.83. This job looks worth it in the long run.
- Equation for the nth dayy=2^{n-1}=pennies y=2^{n-1}/100 dollarsDays=n
- April
- A person comes to you and offers you a job working full time, every day for the month of April. She says she will pay you 1 penny the first day, 2 pennies the second day, 4 pennies the third day, 8 pennies the fourth day and so on, doubling your pay every day. Would you take the job?
- I'll take the job.
- Good. You'll start Sunday.
- How much will you earn for the first week? What is an equation that will tell how much you will get paid on the nth day? How much have you made for 2 weeks’ work? Do you think the job is worth it? Show a calendar with the amount (in dollars, not cents) you will get paid for each day.
- Formula: A=P(1+r/n)^{nt}A=5,368,709.12(1+0.03/4)^{4x20}A=5,368,709.12(1+0.075)^{80}A=5,368,709.12(1.81804398039)A=9,760,549.30
- I'll have $9,760,549.30 in 20 years!
- Create a graph showing the pay for the first week.
- It drops that much!
- Formula: y=C(1-r)^{t}y=41,943.04(1-0.15)^{6}y=41,943.04(0.85)^{6}y=41,943.04(0.37714951)y=15,818.80
- What is your final decision on accepting the job?
- If you take just the last day’s pay and put it in a savings account that pays 3% interest compounded quarterly, leaving it there for 20 years, how much money will you have in the account? “Show work”. Create a graph the shows the first 5 years of the account.
- Depreciation is a ‘decay’ in the value of an item. Suppose you take the 23rd day’s pay and buy a new car. Use this model to find the value of the car after 6 years if it depreciates 15% per year. “Show work”. Create a graph to show the depreciation of the car.