by: mr. kanauss algebra teacher at monongahela middle school

By: Mr. KanaussAlgebra teacher at Monongahela Middle School

Think to yourself what your dream job would be It could be any profession you want It could be working for any person you want The galaxy is the limit

Write down what your dream job is at the top of your page.

I will be giving you this job for 30 days!!

You have to decide what payment option you would like for your paycheck:

1. One cent on the first day, two cents on the second day, and double your salary every day thereafter for the thirty days; or

2. Exactly $5,000,000. (That's five million dollars!)

How many of you are jumping out of your seat for the $5,000,000/mo.?

I would be if I were you!!! I must be a moron or something

Or am I?!?!? Let’s find out…

Let’s look at the first payment option

Paycheck with the first option – Week 1

Day No.

Pay for the Day Total pay in $$

1 .01 .01

2 .02 .03

3 .04 .07

4 .08 .15

5 .16 .31

6 .32 .63

7 .64 1.27

So, for one week of work, you have earned $1.27!!! If you work a 40 hour week (which is normal

work week), how much have you made per hour??

So far, how do you like this payment plan?? Does anyone want to change their mind and

go with the $5,000,000/mo.??

Let’s look at the second week’s pay…

Paycheck with the first option – Week 2

Day No.

Pay for the Day Total pay in $$

8 1.28 2.55

9 2.56 5.11

10 5.12 10.23

11 10.24 20.47

12 20.48 40.95

13 40.96 81.91

14 81.92 163.83

So after 2 weeks we are up to $163.83. If you work a 40 hour week (which is normal

work week), how much have you made per hour??

Now, how do you like this payment plan?? Does anyone want to change their mind and

go with the $5,000,000/mo.??

Let’s look at the third week’s pay

Paycheck with the first option – Week 3

Day No.

Pay for the Day Total pay in $$

15 163.84 327.67

16 327.68 655.35

17 655.36 1,310.71

18 1,310.72 2,621.43

19 2,621.44 5,242.87

20 5,242.88 10,485.75

21 10,485.76 20,971.51

So after 3 weeks we are up to $20,971.51. If you work a 40 hour week (which is normal

work week), how much have you made per hour??

Now, how do you like this payment plan?? Does anyone want to change their mind and

go with the $5,000,000/mo.??

Let’s see how we are looking after four weeks!

Paycheck with the first option – Week 4

Day No.

Pay for the Day Total pay in $$

22 20,971.52 41,943.03

23 41,943.04 83,886.07

24 83,886.08 167,772.15

25 167,772.16 335,544.31

26 335,544.32 671,088.63

27 671,088.64 1,342,177.27

28 1,342,177.28 2,684,354.55

So after 4 weeks we are up to $2,684,354.55!! That’s well over 2 million dollars!! If you work a 40 hour week (which is normal

work week), how much have you made per hour??

Now, how do you like this payment plan?? Does anyone want to change their mind and

go with the $5,000,000/mo.??

Guess what?!?! Here’s the good news…

We still have the last 2 days!!

Paycheck with the first option – Last 2 days!

Day No.

Pay for the Day Total pay in $$

29 2,684,354.56 5,368,709.11

30 5,368,709.12 10,737,418.23

In 30 days, it increases from 1 penny to over 10 million dollars. That is absolutely amazing!!

This mathematical relationship is known as an exponential relationship.

Here is the graph! Equation:

Total Pay = 2n - 1

Here is what 1,003,776 pennies ($10,037.76) looks like

Here is what 10,017,024 pennies ($100,170.24) looks like

Here is what 100,016,640 pennies ($1,000,166.40) looks like –think of a whale here

Here’s what 1,000,018,176 pennies ($10,000,181.76) looks like

10 billion pennies - $100,000,235.52

One Hundred Billion Pennies - $1,000,000,000.00

Two Hundred Billion Pennies - $2,000,000,000.00

One trillion pennies - $10,000,000,000.00

1.8 trillion pennies 2.6 trillion pennies

1 quadrillion pennies 1 quintillion pennies